FIN-110 (3)
@@@ WHYYYY should it be $956.94 A $1000, 7.5% coupon bond has 19.5 years remaining until maturity. Calculate the bond discount if the required return in the bond market is 8.6% compounded semiannually.
$103.14 I did: N = 19.5 x 2 i/y = 8.6 / 2 PMT = (1,000 x 0.075) / 2 FV = 1,000 CPT PV = 956.94
@ check with chegg A New Brunswick Power bond issue carrying a 7.6% coupon matures on November 1, 2031. At what price did $1000 face value bonds trade on June 10, 2019, if the yield to maturity required by the bond market on that date was 5.9% compounded semiannually?
$1156.12 @getting $1,148 so 8 dollars off.. Check with chegg
A $1000, 6.5% coupon, 20-year Government of Canada bond was issued on June 15, 2016. At what price did it trade on December 10, 2020, when the market's required return was 5.2% compounded semiannually?
$1168.86
A $25,000 home improvement (mortgage) loan charges interest at 6.6% compounded monthly for a three-year term. Monthly payments are based on a 10-year amortization and rounded up to the next $10. What will be the principal balance at the end of the first term?
$18,947.10
@check chegg Four and one-half years ago, Glenda purchased 15 $1000 bonds in a Province of New Brunswick issue carrying an 8.5% coupon and priced to yield 9.8% (compounded semiannually). The bonds then had 18 years remaining until maturity. The bond market now requires a yield to maturity on the bonds of 8.0% compounded semiannually. If Glenda sells the bonds today, what will be the dollar amount of her capital gain or loss?
$2246.55
You are considering an investment that will cost $250,000 and generate returns of $60,000 per year for the next 5 years. Calculate the NPV of the investment using a cost of capital of j1=7.0%. Round your answer to the nearest dollar.
-3,988
Andy's Fishing Charters is considering the purchase of a new boat costing $60,000. The boat is expected to increase profits by $9,000 per year for each of the next 8 years. After 4 years, the boat will require maintenance of $6,000. After the 8 years, the boat will be sold for $30,000. Calculate the NPV of the boat using a cost of capital of 12%. Round your answer to the nearest dollar.
-6,988
Acme Industries is considering a project that will cost $200,000 and generate returns of $45,000 at the end of year 1, $85,000 at the end of year 2, $65,000 at the end of year 3 and $30,000 at the end of year 4. Calculate the NPV of the project using a cost of capital of j1=7.0%. Round your answer to the nearest dollar.
-7,755
Nora is thinking about buying a small business for $100,000. She expects to earn profits of $10,000 per year for 5 years and then sell the business for $115,000 (also at the end of the fifth year). Calculate the IRR for the business. Round your answer to the nearest percent.
12
Two and one-half years ago, Nova Scotia Power sold an issue of 25-year, 8% coupon bonds. If the current semiannually compounded return required in the bond market is 6.9%, calculate the percent capital gain or loss on the bonds over the entire 2.5 year holding period
12.48%
A capital investment requiring one initial cash outflow is forecast to have the operating profits listed below. The investment has an NPV of $20,850, based on a required rate of return of 12%. Calculate the payback period of the investment: Year 1 Operating Profit: $74,000 Year 2 Operating Profit: $84,000 Year 3 Operating Profit: $96,000 Year 4 Operating Profit: $70,000
2.7 years
Calculate the payback period for a project that costs $85,000 and returns $25,000 at the end of each year. Express your answer in years rounded to 2 decimal places.
3.40
Calculate the payback period for a project that costs $70,000 and returns $18,000 at the end of each year. Express your answer in years rounded to 2 decimal places.
3.89
You are considering an investment that will cost $15,000 and generate returns of $4,000 at the end of year 1, $5,000 at the end of year 2, $6,000 at the end of year 3 and $3,000 at the end of year 4. Calculate the NPV of the investment using a cost of capital of j1=6.0%. Round your answer to the nearest dollar.
638
An investment opportunity requires an initial cash outlay of $70,000. Thereafter, it is expect to earn profits of $15,000 per year for 6 years. Calculate the IRR for the investment. Express your answer as a percent rounded to 2 decimal places but don't include the % sign.
7.69
@@The City of Victoria has just issued $900,000 in 10-year bonds. As part of the bond contract, the City needs to establish a sinking fund to ensure they have enough funds to pay the bond principal when it comes due. Assume the City of Victoria will make deposits at the end of every six months into an account that will earn j2 = 4.0% What will be the book value of the sinking fund after five years? (hint: requires 3 steps)
@@This was Ch.16 Bond and Sinking Funds pop quiz 2 bonus question - try to get answer but then x2 check with Stan for official answer
A bond is best classfiied as: a debt instrument. an equity instrument. a government revenue instrument.
A Debt instrument
^^^Important^^^ Monica borrowed $5,000 and agreed to pay back the loan with monthly payments over 2 years at 3% compounded monthly. Calculate her monthly payment (rounded up to the next cent). How much principal did she repay during the first year of the loan? How much interest did she repay during the first year of the loan?
A) TVM END PV = -5,000 i/y = 3/12 N = 2x12 CPT PMT = 214.91 B) TVM END PV = -5,000 i/y = 3/12 N = 12 PMT = 214.91 CPT FV = 2,527.40 Principal paid: 5,000 - 2,527.40 = $2,462.60 C) Total amount paid: 214.91 x 12 = 2,578.92 2,578.92 - 2,462.60 = $116.32
Firm A issues $4 million in bonds (4000 certificates of $1000 par value) with a term to maturity of 20 years. At the time of issue, investors demanded a return of 8% compounded semi-annually on investments of similar risk to Firm A. Thus, Firm A decided to set the coupon rate of their bonds at 8% compounded semi-annually A) What is the value of the bond at the time of issue? B) FIVE years later, inflation has risen by 1 percent. Therefore, the YTM on this bond is now 9%. What is the value of the bond? C) Assume that TEN years later inflation has fallen by 2% from five years ago. What is the value of the bond now? D) Calculate your total yield from Year 5 to Year 10, as well as the capital gains yield and interest yield
A) $1,000 value of bond (this means bonds are usually issued at par by issuers) B) $918.56 value of bond (as interest rates go up, the bond prices go down) i.e. selling at discount C) $1,071.06 (As interest rates go down, bond prices go up) i.e. selling at a premium D) 60.15%
Borland Engineering plans to undertake a $900,000 expansion six years from now. By that time, Borland wants to accumulate half of the cost of the expansion by making payments into a sinking fund at the end of each of the next six years. It is anticipated that the money in the sinking fund will earn 7% compounded annually. a) What should be the size of the annual payments? b) What will be the balance after 5 years (use both sinking fund schedule table and TVM) c) At the end of six years, how much of the money in the sinking fund will be interest earnings?
A) $62,908.11 annual PMT B) $361,768.13 (find using both sinking fund table then via TVM) c) $72,551.34
Consider a loan of $2,000 charging interest at j12=4.8% with monthly payments of $87.50.Calculate the missing amounts in the amortization table. Look at file "Loan Amort Table"
A: 1,920.50 x (4.8%/12) = $7.68 B: 87.50 - 7.68 = $79.82 C: 1,920.50 - 79.82 = $1,840.68
You have a 5 year loan for $15,000 at j2 = 3%, with semi annual payments of $1,626.513. What will the balance be after the fourth year?
Balance after 2nd to last payment: TVM END N = 4x2 i/Y = 3/2 PV = -15,000 PMT = 1,626.513 CPT FV = 3,181.27
Bonds A and C both have a face value of $1,000 and pay a coupon rate of 6.7%. They have 5 and 20 years, respectively, remaining until maturity. Calculate the yield to maturity of each bond if its purchased for $950
Bond A: N = 5x2 PMT = (1,000 x 6.7%) / 2 PV = -950 FV = 1,000 CPT i/y = 3.965 3.965 x 2 = *7.93%* Bond B: N = 20x2 PMT = (1,000 x 6.7%) / 2 PV = -950 FV = 1,000 CPT i/y = 3.585 3.585 x 2 = *7.17%*
Best-Buy Computers advertises a popular laptop computer for $1,999.95. The same system may be leased for 24 months at $99 per month (at the beginning of each month). At the end of the lease, the system may be purchased for 10% of the retail price. Should you lease or purchase the computer if you obtain a two-year loan at 7% compounded annually to purchase the computer?
Buy it upfront as the PV would be less (and cost less) at $1999.95 than at $2,403.205
A potential project requires an initial investment of $2,000. You have estimated that the project will result in cash flows of $1,100 in each of the next two years. If your required rate of return on the project is 11%, what is the Net Present Value for the project?
CFo = -2,000 C01 = -1,100 F01 = 2 I = 11 CPT NPV = -$116.22
You are thinking of starting a retail business. You estimate you will need to invest $50,000 to secure some physical space, and then renovate and stock it. After sitting down with your business partner, your best estimates for cash flow over the next five years is as follows: Year 1: $5,000 Year 2: $7,000 Year 3: $12,000 Year 4: $19,000 Year 5: $24,000 Assuming a cost of capital of 8.0%, and five years of sweat equity as a self-employed entrepreneur, calculate the net present value of your business opporunity. Would you proceed with starting your business? (yes/no)
CFo = -50,000 CO1 = 5,000 CO2 = 7,000 CO3 = 12,000 CO4 = 19,000 CO5 = 24,000 I = 8% CPT NPV = $456.55 No.. while it is greater than 0, a five year commitment for $456.55 is just not worth it for most. But it could be worth it for some so "it depends"
On February 4, 2019, Auston Matthews of the Toronto Maple Leafs signed a contract extension where he will earn an average annual salary of $11.63 million per year. The contract amounts to a total of $58.15 million over 5 years. Year-by-year summary of Matthew's contract: [See "Auston" picture] Assuming a discount rate of j1 = 4.0%, what is the economic value of Auston's contract (on the day he signed it)?
Could also go: Year 5: N = 1 i/y = 4 PMT = 7950 CPT PV = 7644.23 Year 4: FV = 7644.23 N = 1 i/y = 4 PMT = 7950 CPT PV = 14,994.45 Etc... but this method takes way longer
^^ important Four years ago, you purchased a Government of Canada bond with a coupon rate of 3.5% and 20 years to matuirty. AT the time, your required rate of return on investments of similar risk was 3.75%. Today, inflation has gone down by 1% from four years ago (how does that affect your required rate of return?). If you sold the bond today, calculate your TOTAL RETURN on your investment (Hint - requires 3 steps)
Four years ago: N - 20x2 i/y = 3.75/2 PMT = (1,000 x 3.5%) / 2 FV = 1,000 CPT PV = -965.04 Today: N = 16x2 i/y = 2.75/2 PMT = (1,000 x 3.5%) / 2 FV = 1,000 CPT PV = -1,096.55 Capital gain yield = 1,096.55 - 965.04 / 965.04 = 13.63% Interest yield: (17.5 x 2 x 4) / 965.04 = 14.51% Total: *28.14%*
The Delgados have a gross monthly income of $7,000. Monthly payments on personal loans total $500. Their bank limits the gross debt service ratio at 33% and the total debt service ratio at 42%. What is the maximum 25-year mortgage loan for which they can qualify on the basis of their income? Assume monthly heating costs of $200 and property taxes of $220 per month. Current mortgage rate are 6.8% compounded semi-annually
GDS: (33% x 7,000) - (200+220) = 1890 TDS (42% x 7,000) - (200+220) - 500 = 2020 Use GDS of 1890 as it's the lower amount TVM END N = 25x12 I/y = i2 = (1 + 0.068/2)^2/12 - 1 = 0.5588101773 PMT = 1890 CPT PV = 274,664.69*$274,664.69*
A machine shop is trying to decide which of two types of metal lathe to purchase. The more versatile Japanese lathe costs $32,000, and will generate an annual profit of $16,000 for three years. Its trade-in value after three years will be about $10,000. The more durable German lathe costs $42,000, and will increase profits by $12,000 per year for six years. Its trade-in value at that point is estimated at $15,000. Assuming a cost of capital of 10%, use the Replacement Chain method to decide which lathe should be purchased. What is the difference in net present value between the two projects?
Go with the Japanese option at $26,799.98 NPV which is greater than the German NPV of $18,730.24
A $600,000 capital investment will produce annual profits of $90,000 for the first four years and $120,000 for the next four years. It will have no residual value. What is its IRR? Should investments be undertaken if the cost of capital is 7%?
IRR = 7.6%. The investment should be undertaken since its IRR is greater than the cost of capital (7%)
Half way through its term, the balance in a sinking fund will be: half of the goal (future value). less than half of the goal (future value). more than half of the goal (future value).
Less than half of the goal (future value) - because interest keeps growing and gets bigger and bigger - think of sinking fund schedule
Increasing your regular loan payments by 10% will shorten the loan amortization period by: more than 10%. less than 10%. 10% exactly.
More than 10%
Rick just purchased a ten year, $5,000 bond with a 4% coupon rate for $4,930. Calculate the yield rate that Rick will earn (nominal, semi-annual).
N = 10x2 PV = -4,930 PMT = (5,000x4%) / 2 FV = 5,000 CPT i/y = 2.086334401 x 2 = *4.17%* compounded semi-annually
A 10 year, $5,000 bond with a coupon rate of j2=5% is priced at $5,215. What yield to maturity (j2) will an investor realize if they purchase the bond? Round your answer to 2 decimal places and express as a percentage. Use either trial and error or interpolation.
N = 10x2 PV = -5,215 PMT = (5,000 x 5%) / 2 FV = 5,000 CPT i/y then x 2 = *4.46%*
A company just issued a ten-year, $10,000 bond with a coupon rate of j2=6.60%. What price would an investor be willing to pay for the bond if they wanted a return on their investment of j2=10%?
N = 10x2 i/y = 10/2 PMT = (10,000 x 6.60%0 / 2 FV = 10,000 CPT PV = $7881.42
The City of Victoria has just issued $800,000 in 10-year bonds. They are required to establish a sinking fund in order to save enough money to pay the bond redemption when it comes due. How much must they deposit at the end of every six months into an account earning j2=4% in order to save the $800,000?
N = 10x2 i/y = 4/2 FV = 800,000 CPT PMT = $32,925.37
Four years ago, Gavin purchased $25,000 of a new 20-year Province of Ontario bond with a 6.1% coupon rate at par. If he sold the bond today at a price of $21,823.98, what was his yield to maturity on the bond? (nominal rate compounded semi-annually)
N = 16x2 PV = -21,823.98 PMT = (25,000 x 6.1%) / 2 FV = 25,000 CPT i/y = 3..73718187 3.73718187 x 2 = *7.47%*
A company is planning on spending $27,000 to upgrade their computer systems in 4 years time. How much must they deposit monthly into an account earning j12=3% in order to have enough money for the new computers?
N = 4x12 i/y = 3/12 FV = 27,000 CPT PMT = $530.13
MegaCorp just issued a five-year, $20,000 bond with a coupon rate of j2=4.68%. What price would an investor be willing to pay for the bond if they wanted a return on their investment of j2=8%?
N = 5x2 i/y = 8/2 PMT = (20,000 x 4.68%) / 2 FV = 20,000 CPT PV = $17,307.18
A new machine that will lead to savings in labour costs of $20,000 per year can be purchased for $80,000. However, it will cost $2000 per year for the first four years, and $3000 per year for the next four years to service and maintain the machine. In addition, its annual fuel consumption will cost $1500. After a service life of eight years, the salvage value of the machine is expected to be $10,000. Should the machine be acquired if the company requires a minimum annual rate of return on investment of 8%?
NPV = $17,788. The machine should be acquired
A proposed open-pit mine would require the investment of $3 million at the beginning of the first year and a further investment of $1 million at the end of the first year. Mining operations are expected to yield annual profits of $750,000, beginning in Year 2. The ore body will sustain eight years of ore extraction. At the beginning of the tenth year, the mining company must spend $1 million on cleanup and environmental restoration. Will the project provide the mining company with a rate of return exceeding its 5.5% cost of capital?
NPV = -$62,250. The project will not provide a rate of return exceeding 5.5%
An investor requires a return of 15% on projects that she invests in. She has looked at a potential project and calculated that the internal rate of return (IRR) for the project is 12%. The correct decision would be to: proceed with the project because the IRR is smaller than her required rate of return. not invest in the project because the IRR is lower than her required rate of return. proceed with the project because the IRR is still larger than 10%.
Not invest because IRR is lower than her required rate of return
Machine X costs $50,000 and its forecast to generate an annual profit of $16,000 for five years. Machine Y, priced at $72,000, will produce the same annual profit for ten years. The trade-in value of X after five years is expected to be $10,000, and the resale value of Y after ten years is also thought to be $10,000. If either machine satisfies the firm's requirements, which one should be selected? Use a required return of 8%
PMT(X) = $5182. PMT(Y) = $5960 Machine Y should be selected because its equivalent annual cash flow is $778 larger
A potential project has a net present value (NPV) of $28,356. This amount includes the initial cash outlay of $30,000. The correct decision would be to: cancel the project because the NPV is lower than the initial cash outlay. proceed with the project because the NPV is positive.
Proceed
A company's board of directors has imposed an $800,000 limit on capital spending for the current year. Management has identified the following five projects with positive NPVs. Which projects should be chosen? [See "NPV" picture for table]
Projects A, D, and C give the highest aggregate NPV within the $800,000 capital budget constraint
The investment committee of a company has identified the following seven projects with positive NPVs. The board of directors has approved a $3 million capital budget for the current period. [See "comparing" picture] a) Which projects should be selected? b) What will be the total value added (NPV) to the firm as a result of the projects selected?
Projects: 1,4,3,5,6 NPV: $1,289,000
A firm can manufacture the same product with either of two machines. Machine C requires an initial investment of $55,000 and would earn a profit of $30,000 per year for three years. It would then be replaced, because repairs would be required too frequently after three years. Its trade-in value would be $10,000. Machine D costs $90,000 and would have a service life of five years. The annual profit would be $5000 higher than Machine C's profit because of its lower repair and maintenance costs. Its recoverable value after five years would be about $20,000. Which machine should be purchased if the firm's cost of capital is 9%? What is the equivalent annual economic advantage of the preferred choice?
Purchase Machine D because it has a $3880 larger annual economic advantage
Rainbow Aviation needs an additional plane for five years. It can buy the plane for $360,000 using funds borrowed at 7.5% compounded monthly, and then sell the plane for an estimated $140,000 after five years. Alternatively, it can lease the plane for $5600 per month, payable at the beginning of each month. a) Which alternative should Rainbow Aviation choose? b) What is the financial advantage of the preferred alternative?
Rainbow Aviation should purchase the plane and thereby gain an economic advantage (in current dollars) of $17,549
Consider a mortgage on a home. Will you repay more principal in the third year or the sixth year? Third year. Sixth year. Neither, the amount will be the same in both years.
Sixth year As it starts - interest high principal low - as mortgage goes on interest payments lower progressively and principle higher progressively
Joanna purchased a 20-year annuity with $100,000 accumulated in her RRSP. At a rate of 5.6% compounded quarterly, she will receive equal payments of $2,085.891 at the end of every calendar quarter Of the payments received in the 10th year, what dollar amount represents the recovery of principal from her initial investment of $100,000?
Step 1: Balance at end of year 9 N = 9x4 i/y = 5.6/4 PV = -100,000 PMT = 2,085.89 CPT FV = 68,176.94 Step 2: Balance at end of year 10 N = 10x4 i/y = 5.6/4 PV = -100,000 PMT = 2,085.89 CPT FV = 63,555.36 Step 3: Recovery of principal in year 10 = Balance Year 9 - Balance Year 10: 68,176.94 - 63,555.36 = $4,621.58 (recovery of principle - our own cash the bank is returning to us)
^^ important - method maybe on CS? seems simple but also easy to write down A $40,000 loan at 6.6% compounded monthly will be repaid by monthly payments over 10 years. Calculate the interest component of Payment 35
Step 1: Find missing component: TVM END N = 10 x 12 PV = -40,000 i/y = 6.6/12 CPT PMT = 456.23 Step 2: Find ending balance after 34th payment: TVM END N = 34 PV = -40,000 i/y = 6.6/12 PMT = 456.23 CPT FV = 31,194.65 Step 3: Find missing interest component on the 35th payment: Balance after 34th payment x periodic interest rate: 31,194.65 x (0.066/12) = $171.57
Ace Industries borrowed $150,000 amortized over 10 years at a rate of j12=4.8% with monthly payments (rounded up to the next cent). Calculate their final payment.
TVM PV = -150,000 N = 10x12 i/Y = 4.8/12 CPT PMT = $1,576.36 (although for quiz it says 1,576.26 so put that if reasked it - it's wrong though) If given 110,000 - offical answer is "1,155.52" @what is the "final payment" - ask prof for final exam prep - if it's just simple rounding error on his part ask for 10/10 on chapter 15 quiz for attempt #2
A mortgage contract for $50,000 with an amortization period of 25 years was written five years ago. The interest rate for the first 5-year term was j2=8%. The mortgage is just at the end of its first five-year term, e.g. today. Assuming monthly payments (normal for mortgage contracts), calculate the principal balance today
TVM END N = 25x12 PV = -50,000 I/y=I/2 = (1+0.08/2)^2/12 - 1 = 0.655819694 CPT PMT = 381.6067 TVM END N = 5x12 PV = -50,000 I/Y = 0.655819694 PMT = 381.6067 CPT FV = 46,067.88161 *$46,067.88*
Tim borrowed $15,000 at a rate of 7.34% compounded semi-annually (j2). Calculate his monthly payments if he amortizes his payments over 5 years.
TVM END PV = -15,000 i/y = i2 = (1 + 0.0734/2)^2/12 - 1 N = 5x12 CPT FV = $298.65
Chandler borrowed $18,800 and agreed to repay the loan with payments of $450 per month. Using an interest rate of j12=3.6%, calculate the amount of principal repaid during the first year of the loan.
TVM END PV = -18,800 PMT = 450 i/y = 3.6/12 N = 12 CPT FV = 13,998.08 Principle = 18,800 - 13,998.08 = *$4801.92*
Amrit is thinking about buying a new car. The car sells for $25,000 and he has a $3,000 down-payment. Calculate his monthly payments if he amortizes the balance at j12=3.6% over 5 years.
TVM END PV = -22,000 i/y = 3.6/12 N = 5x12 PMT = 401.20
Lisa borrowed $25,000 at a rate of 6% compounded monthly (j12) for a term of 10 years. Calculate the balance owing on her loan after 6 years. When calculating her original payment, round it up to the next cent before proceeding to the balance calculation
TVM END PV = -25,000 i/y = 6/12 N = 10x12 CPT PMT = 277.56 TVM END PV = - 25,000 PMT = 277.56 i/y = 6/12 N = 6x12 CPT FV = $11,817.46
A couple has a $420,000 mortgage amortized over 30 years with monthly payments. They chose to lock in a rate of j2=4% for the first 5 years. Calculate their new monthly payment (rounded up to the next cent) if they refinance at j2=5.50% after the first 5 years are up.
TVM END PV = -420,000 N = 30x12 i/Y = i2 = (1+0.04/2)^2/12 - 1 = 0.330589033 CPT PMT = 1,997.178538 TVM END PV = -420,000 N = 5x12 i/Y = 0.330589033 PMT = 1,997.178538 CPT FV = 379,677.1527 TVM END PV = -379,677.1527 N = 25x12 i/y=i2 = 0.453168172 CPT PMT = 2,317.517002 = *$2,317.52*
Tai consolidated her outstanding debt into a low-interest personal loan of $50,000 at a rate of 6% compounded monthly (j12) for a term of 10 years. How much will she owe on her loan after 4 years of payments? When calculating her original payment, round it up to the next cent before proceeding to the balance calculation.
TVM END PV = -50,000 i/y = 6/12 N = 10x12 CPT PMT = 555.11 TVM END PV = -50,000 PMT = 555.11 i/y = 6/12 N = 4x12 CPT FV = 33,494.21 *$33,494.21*
@chegg TVM function give them answer to work from The provincial government's Ministry of Fisheries requires a new patrol boat. The price of a Songster is $90,000, and its annual operating costs will be $10,000. It will be sold for about $20,000 after five years, and replaced. A more durable and more efficient Boston Wailer, priced at $110,000, would cost $8000 per year to operate, last seven years, and have a resale value of $40,000. If the provincial government pays an interest rate of 6.5% compounded annually on its midterm debt, which boat has the lower equivalent annual cost?
The Boston Wailer's equivalent annual cost is $4781 lower
@ CS Who is, and who is not subject to a mortgage stress test for a new buyer looking to purchase a home?
The only one NOT SUBJECT to a stress test: 1. Down Payment >20% & have an existing mortgage Three SUBJECT to a stress test: 1. Down Payment >20% & new mortgage 2. Down payment <20% & existing mortgage 3. Down Payment <20% and new mortgage
If we round up our regular loan payments, the final payment will always be smaller. True False
True
The internal rate of return (IRR) is the discount rate that results in a net present value (NPV) of zero. True False
True
When you make a lump sum payment on a loan, the entire amount goes towards reducing the balance owing. True False
True
With amortization, each payment consists of both principal and interest amounts. True False
True
When prevailing market rates decline over the time an investor owns a bond, there is often an opportunity to receive a capital gain on the sale of the bond. True False
True Could take one interest rate and calculate PV then a lower one and caluclate PV then calculate the capital gains yield and if positive then yes - which it is
The interest earned in a sinking fund grows with each deposit. True False
True - interest keeps growing
That is what the formula is telling us... Lilly agreed to repay a loan of $29,500 with payments of $475 per month. Using an interest rate of j12=3.6%, calculate the amount of principal repaid during the second year of the loan.
Year 1 principle: TVM END PV = -29,500 PMT = 475 i/Y = 3.6/12 N = 12 CPT FV = 24,784.70254 Year 2 principle: TVM END PV = -29,500 PMT = 475 i/Y = 3.6/12 N = 2x12 CPT FV = 19,896.82528 24,784.70254-19,896.82528= $4,887.88
^^^ Important ^^^ @ payback period - get chegg AND prof help on Investment proposals A and B require initial investments of $45,000 and $35,000, respectively. Both have an economic life of four years with no residual value. Their expected profits are as follows: [see "proposal" picture"] If the firm's cost of capital is 14%, rank the proposals based on their (i) net present value; (i)internal rate of return; (iii) profitability index; (iv)payback period. Which is overall better?
[NOTE: A is better for NPV and Payback period and B is better for Profitability Index and IRR - IF THIS IS EVER THE CASE WE TAKE WHICHEVER HAS THE BETTER (HIGHER) NPV AS IT'S MORE INFORMATIVE SO WE SAY A IS BETTER] A IS BETTER
Golden Dragon Restaurant obtained a $10,000 loan at 9% compounded annually to replace some kitchen equipment. Prepare a complete amortization schedule if the loan is repaid by semi-annual payments over a three-year term. (Hint: using two decimals throughout you should get within $3.00 of paying down the loan)
[need answer - from pop quiz 1]
Stan has a $350,000 mortgage amortized over 25 years with monthly payments. He secured a rate of j2=3.25% for the first 5-year term. Calculate Stan's new monthly payment for the second 5-year term if he refinances his mortgage at j2=4.0% Hint: Requires at least three (possibly five) calculations to arrive at the final answer.
[need answer for - this was from pop quiz bonus question]
The initial investment and expected profits from two mutually exclusive capital investments being considered by a firm are as follows: [See "fin invest" table] a) Calculate the internal rate of return for each investment. Which one would be selected based on an IRR ranking? b) Which investment should be chosen if the firm's cost of capital is 10%? c) Which investment should be chosen if the firm's cost of capital is 7%?
a) IRR on Investment A = 11.0% IRR on Investment B = 11.6% Investment B would be selected on the basis on an IRR ranking b) NPV (investment A) = $1388 NPV (investment B) = $1777 Investment B has the larger NPV and should be chosen c) NPV (Investment A) = $5912 NPV (Investment B) = $5401 Investment A now has the higher NPV and should be chosen
^^ important Stan signed a contract for a $9,500 personal loan at 7.5% compounded monthly, to be repaid over a four-year term by equal monthly payments. a) Calculate the interest and principal components of the twenty-eighth payment. b) How much (total) interest did he pay in the second year of the loan?
a) Interest component of the 28th period: Step 1: Find the payment (missing component) TVM END N = 4x12 i/Y = 7.5/12 PV = -9,500 CPT PMT = 229.70 Step 2: Find ending balance after 27th payment TVM END N = 27 i/Y = 7.5/12 PV = -9,500 PMT = 229.70 CPT FV = 4,507.36 Step 3: Interest paid in the 28th payment: Balance of 27th payment x periodic interest rate = 4,507.36 x (0.075/2) = 28.17 Step 4: Principal paid of the 28th payment: Payment - Interest Paid = 229.70 - 28.17 = $201.53 b) Total Interest Paid in the 2nd year of the loan: Step 1: Find total amount paid in Year 2 = Payments x 12 = 229.70 x 12 = 2,756.40 Step 2: Find the balance at the end of Month 12: N = 12 i/y = 7.5/12 PV = -9,500 PMT = 229.70 CPT FV = 7,384.36 Step 3: Calculate the balance at the end of Month 24: N = 24 i/y = 7.5/12 PV = -9,500 PMT = 229.70 CPT FV = 5,104.47 Step 4: Interest paid in year 2 = Total Paid - Principal Paid = Total Paid - (Balance Month 12 - Balance Month 24) = 2,756.40 - (7,384.36 - 5,104.47) = $476.514
Marpole Carpet Cleaning borrowed $7,600 from Richmond Credit Union at 8% compounded quarterly. The loan is to be repaid by equal quarterly payments over an 18-month term. a) What is the quarterly payment amount? Round your answer to 2 decimals. b) Construct the loan amortization table for the loan c) Use the Retrospective method to find the balance after the 3rd period
a) N = 18/3 = 6 (how many quarterly periods are there? there are 6 in an 18 month period) i/y = 8/4 PV = -7,600 CPT PMT = 1,356.80 b) picture c) N = 3 i/Y = 8/4 PV = -7,600 PMT = +1,356.796 CPT FV = $3,912.84 Retrospective method allows us to find the balance of the loan at ANY TIME (could have up to 300 payments - if they ask to find at the 246 PMT - we can use this method to find that)
^ important and need to figure out how got the capital gain yield for CS @@ Three years after the issue of a $10,000, 6.5% coupon, 25-year bond, the rate of return required in the bond market on similar long-term bonds is 5.8% compounded semi-annually a) What price would the bond sell for today? b) Calculate the interest yield (%), capital gain (or loss) yield (%), and total yield (%) assuming the owner bought the bond at the time of issue and sold the bond today.
a) N = 22x2 i/y = 5.8/2 PMT = (10,000 x 6.5%) / 2 FV = 10,000 CPT PV = $10,863.82 b) i) Interest yield: (325x2x3) / 10,000 = 19.5% ii) Capital Gain Yield: (10,863.82 / 10,000) / 10,000 = 8.64% iii) Total yield: 19.5% + 8.64% = 28.14%
An annuity providing a rate of return of 4.8% compounded monthly was purchased for $45,000. The annuity pays $400 at the end of each month. a) How much of Payment 37 will be interest? b) What will be the principal portion of Payment 92? c) How much interest will be paid by Payments 85 to 96 inclusive? d) How much principal will be repaid in the fifth year? e) What will be the amount of the final payment?
a) $146 b) $316.37 c) $1025.91 d) $3268.88 e) $303.34
Meditech Laboratories borrowed $28,000 at 10% compounded quarterly to purchase new testing equipment. Payments of $1500 are made every three months. a) Calculate the balance after the tenth payment b) Calculate the exact amount of the final payment
a) $19,037.29 b) Step 1: Find the number of payments for this loan (missing component) TVM END i/y = 10/4 PV = -28,000 PMT = +1,500 CPT N = 25.46 periods (ALWAYS ROUND YOUR ANSWER FOR N UP TO THE NEXT WHOLE INTEGER OR HE'LL TAKE MARKS OFF) N = 26 periods = 26 payments - what was the amount of the last payment (the 26th payment) Step 2: Find the balance at the 2nd to last payment (25th payment) TVM END N = 25 i/y = 10/4 PV = -28,000 PMT = +1,500 CPT FV = 673.789 Step 3: Find the balance at the last payment (26th payment): Balance after 25th payment x (1 + periodic rate) = 673.78 x (1 + 0.025) = $690.63
A $255,000 amount from an RRSP is used to purchase an annuity paying $6000 at the end of each quarter. The annuity provides an annually compounded rate of return of 2.5% a) What will be the amount of the final payment? b) What will be the interest portion of the 27th payment? c) What will be the principal portion of the 33rd payment? d) How much will the principal balance be reduced by Payments 14 to 20 inclusive? e) How much interest will be received in the sixth year?
a) $2837.08 b) $809.33 c) $5386.53 d) $34,162.12 e) $3805.67
The interest rate for the first five years of a $90,000 mortgage loan is 5.25% compounded semiannually. Monthly payments are calculated using a 20-year amortization. a) What will be the principal balance at the end of the five-year term? b) What will be the new payments if the loan is renewed at 6.5% compounded semiannually (and the original amortization period is continued)
a) $75,367.19 b) $652.96
A $28,000 loan at 8% compounded quarterly is to be repaid by equal quarterly payments over a seven-year term a) What will be the principal component of the sixth payment? b) What will be the interest portion of the 22nd payment? c) How much will the loan's balance be reduced by Payments 10 to 15 inclusive? d) How much interest will be paid in the second year?
a) $834.36 b) $170.31 c) $5697.14 d) $1891.34
^^Important^^ A $100,000 mortgage loan is written with a 20-year amortization period, a 3-year mortgage term, and an interest rate of 4.5% compounded semiannually. Payments are made monthly. a) Calculate the balance at the end of the three-year term b) At the end of the 3-year term, calculate the size of the payments upon renewal for a five-year term at 4% compounded semiannually
a) $90,048.13 (or $90,048.32 depending on rounding of PMT) b) $69,520.71
The interest rate for the first three years of an $87,000 mortgage is 4.4% compounded semiannually. Monthly payments are based on a 20-year amortization. If a $4000 prepayment is made at the end of the 16th month: a) How much will the amortization period be shortened? b) What will be the principal balance at the end of the three-year term?
a) 1 year and 4 months b) $73,956.77
After two years of the first five-year term at 6.7% compounded semiannually, Dan and Laurel decide to take advantage of the privilege of increasing the payments on their $110,000 mortgage loan by 10%. The monthly payments were originally calculated for a 25-year amortization. a) How much will the amortization period be shortened? b) What will be the principal balance at the end of the five-year term?
a) 4 years and 2 months b) $96,786.36
The expected profits from an $80,000 investment are $15,000 in Year 1 and $20,000 in each of Years 2 to 7. a) What is the investment's payback period? b) If the firm's required payback period is four years, will it make the investment? c) If the firm's cost of capital is 8%, will it make the investment based on the NPV criterion?
a) 4.25 years b) No - because the machine's payback period exceeds the required payback of 4 years c) NPV = $19,498 - Yes.. since the NPV is positive, the firm will make the investment
A manufacturer's sales rep can lease an automobile for five years at $385 per month payable at the beginning of each month, or purchase it for $22,500. He can obtain a loan at 9% compounded monthly to purchase the car. Should he lease or buy the car if: a) The trade-in value after five years is $5000? b) The trade-in value after five years is $7000?
a) The car should be leased because the economic value of the net cash outflows is $621 lower b) The car should be purchased (a $657 advantage over leasing)
A loan's balance midway through its amortization period be: less than half of the original principal. equal to half of the original principal. more than half of the original principal.
more than half of the original principal.
