FINAL Money and Credit

CHAPTER 18 Employee plus employer contributions to a 401(k) are $11,000 per year. Equity funds are earning 10 percent; bond funds, 5 percent; and money market funds, 3 percent. The employee will retire in 30 years. How much money will he have if he earns the average return from putting 65 percent of his money in equities, 30 percent in bond funds, and the rest in money market funds?

$1,280,925

CHAPTER 17 An investor purchases a mutual fund for $50. The fund pays dividends of $1.50, distributes a capital gain of $2, and charges a fee of $2 when the fund is sold one year later for $52.50. What is the net rate of return from this investment?

(52.50+1.50+2-2-50)/50 =4/50 =8%

CHAPTER 2 Suppose we observe the three-year Treasury security rate (1R3) to be 5.2 percent, the expected one-year rate next year—E(2r1)—to be 6.2 percent, and the expected one-year rate the following year—E(3r1)—to be 6.8 percent. If the unbiased expectations theory of the term structure of interest rates holds, what is the one-year Treasury security rate?

1 + 1R1 = (1.052)^3/(1.062*1.068) so, 1R1 = 0.0265 = 2.65%

CHAPTER 9 A U.S. bank converted $1 million to Swiss francs to make a Swiss franc loan to a valued corporate customer when the exchange rate was 1.2 francs per dollar. The borrower agreed to repay the principal plus 5 percent interest in one year. The borrower repaid Swiss francs at loan maturity and when the loan was repaid the exchange rate was 1.3 francs per dollar. What was the bank's dollar rate of return?

1) $1,000,000 x (1.2 SF/$1) =SF1,200,000 x (1.05) =SF 1,260,000 2) SF 1,260,000 x ($1/1.3 SF) = $969,230.7692 3) [($969,230.7692- $1,000,000)/$1,000,000] x 100 =-3.0769%

CHAPTER 9 A Swiss bank converted 1 million Swiss francs to euros to make a euro loan to a customer when the exchange rate was 1.85 francs per euro. The borrower agreed to repay the principal plus 3.75 percent interest in one year. The borrower repaid euros at loan maturity and when the loan was repaid the exchange rate was 1.98 francs per dollar. What was the bank's franc rate of return?

1) 1,000,000 SF x (1 E/1.85 SF) =540,540.5405 E x (1.0375) = 560,810.8108 E 2) 560,810.8108 E x (1.98 SF/1 E) = 1,110,405.404 SF 3) [(1,110,405.404 SF - 1,000,000 SF)/1,000,000 SF] x 100 =11.0405%

CHAPTER 9 An investor starts with $1 million and converts it to 0.75 million pounds, which is then invested for one year. In a year the investor has 0.7795 million pounds, which she then converts to dollars at an exchange rate of 0.72 pounds per dollar. Calculate the U.S. dollar annual rate of return earned.

1) 779,500pounds x (1$/.72pounds) =$1,082,638.889 2) [($1,082,638.889-$1,000,000)/$1,000,000] x 100 =8.2639%

CHAPTER 17 Suppose today a mutual fund contains 2,000 shares of J.P. Morgan Chase, currently trading at $64.75, 1,000 shares of Walmart, currently trading at $63.10, and 2,500 shares of Pfizer, currently trading at $31.50. The mutual fund has no liabilities and 10,000 shares outstanding held by investors. What is the NAV of the fund? Calculate the change in the NAV of the fund if tomorrow J.P. Morgan shares increase to $66, Walmart's shares increase to $68, and Pfizer's shares decrease to $30. Suppose that today 1,000 additional investors buy one share each of the mutual fund at the NAV of $27.135. This means that the fund manager has $27,135 in additional funds to invest. The fund manager decides to use these additional funds to buy additional shares in J.P. Morgan Chase. Calculate tomorrow's NAV given the same rise in share values as assumed in (b).

1) NAV=[(2000x64.75) + (1000x63.10) + (2500x31.50)]/10000 = 27.135 2) NAV=[(2000x66) + (1000x68) + (2500x30)]/10000 = 27.50 (27.50-27.135)/27.135 = 1.345% change 3) 27135/64.75 = 419.073 NAV= [(2419.073x66) + (1000x68) + (2500x30)]/11000 = 27.514

CHAPTER 17 Open-end Fund A has 165 shares of ATT valued at $35 each and 30 shares of Toro valued at $75 each. Closed-end Fund B has 75 shares of ATT and 72 shares of Toro. Both funds have 1,000 shares outstanding. What is the NAV of each fund using these prices? If the price of ATT stock increases to $36.25 and the price of Toro stock declines to $72.292, how does that impact the NAV of both funds? Assume that another 155 shares of ATT valued at $35 are added to Fund A. The funds needed to buy the new shares are obtained by selling 676 more shares in Fund A. What is the effect on Fund A's NAV if the prices remain unchanged from the original prices?

1) Open: NAV = [(165x35) + (30x75)]/1000 = 8.025 Closed: NAV = [(75x35) + (72x75)]/1000 = 8.025 2) Open: NAV = [(165x36.25) + (30x72.292)]/1000 = 8.15001 (8.15001-8.025)/8.025 = 1.5578% change Closed: NAV = [(75x36.25) + (72x72.292)]/1000 =7.923774 (7.923774-8.025)/8.025 = -1.2614% change 3) [((165+155)x35) + (30 x 75)]/(1000+676) = 8.025 (8.025-8.025)/8.025 = 0% change

CHAPTER 2 Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:1R1 = 0.5%, E(2r 1) = 1.5%, E(3r1) = 7.7%, E(4r1) = 8.05% Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year maturity Treasury securities.

1-year: 1R1: 0.500% 2-year: 1R2: [(1 + .005) (1 + .015)] ^(1/2) -1 = 0.999% 3-year: 1R3: [(1 + .005) (1 + .015) (1 + .077)] ^(1/3) -1 = 3.185% 4-year: 1R4: [(1 + .005) (1 + .015) (1 + .077) (1 + .0805)] ^(1/4) -1 = 4.380%

CHAPTER 17 Suppose an individual invests $20,000 in a load mutual fund for two years. The load fee entails an up-front commission charge of 2.5 percent of the amount invested and is deducted from the original funds invested. In addition, annual fund operating expenses (or 12b-1 fees) are 0.55 percent. The annual fees are charged on the average net asset value invested in the fund and are recorded at the end of each year. Investments in the fund return 7 percent each year paid on the last day of the year. If the investor reinvests the annual returns paid on the investment, calculate the annual return on the mutual funds over the two-year investment period.

20,000 x (1-.025) = 19500 19500 x 1.07 = 20865 [(19500 + 20865)/2] x .0055 = 111.00375 20865 - 111.00375 = 20753.99625 20753.99625 x 1.07 = 22206.77599 [(20753.99625 + 22206.77599)/2] x .0055 = 118.142 22206.77599 - 118.142 = 22088.63399 FV: 22088.63399 PV: -20,000 N: 2 PMT: 0 CPT: I/Y I/Y = 5.0919

CHAPTER 9 Bank USA recently purchased $11.3 million worth of euro-denominated one-year CDs that pay 11 percent interest annually. The current spot rate of U.S. dollars for euros is $1.104/€1. A) Is Bank USA exposed to an appreciation or depreciation of the dollar relative to the euro? B) What will be the return on the one-year CD if the dollar appreciates relative to the euro such that the spot rate of U.S. dollars for euros at the end of the year is $1.004/€1? C) What will be the return on the one-year CD if the dollar depreciates relative to the euro such that the spot rate of U.S. dollars for euros at the end of the year is $1.204/€1?

A) Appreciation $11,300,000 x (E1/$1.104) = E10,235,507.25 x 1.11 =E11,361,413.05 B) E11,361,413.05 x ($1.004/E1) = $11,406,858.70 [($11,406,858.70-$11,300,000)/$11,300,000] x 100 =0.946% C) E11,361,413.05 x ($1.204/E1) = $13,679,141.31 [($13,679,141.31-$11,300,000)/$11,300,000] x 100 = 21.054%

CHAPTER 7 You plan to purchase a $280,000 house using a 15-year mortgage obtained from your local credit union. The mortgage rate offered to you is 7 percent. You will make a down payment of 10 percent of the purchase price. You are constructing the amortization schedule for the payments. For the sixth month find the following information: a) Beginning Loan Balance b) Payment c) Interest d) Principal e) Ending Loan Balance

A) Beg Loan Balance FV:0 I/Y:7/12 N:175 PMT:2265.05 CPT PV: 247,978.42 B) PMT N:180 I/Y:7/12 FV:0 PV:-252,000 CPT PMT: 2,265.05 C) Interest pmt=loan balance X monthly rate 247,978.42 X (7/12) = 1,446.54 D) Principal PMT = monthly pmt - interest pmt 2265.05 - 1446.54 = 818.51 E) Ending Loan Balance = Beg. Loan Balance - Principal Paid 247,978.42 - 818.51 = 247,159.91

CHAPTER 18 An employee contributes 9 percent of his salary to his 401(k) plan and the employer matches with 40 percent of the first 6 percent of the employee's salary. The employee earns $90,000 and is in a 28 percent tax bracket. If the employee earns 10 percent on the plan investments, what is his one-year rate of return relative to the net-of-tax amount of money he invested?

Balance after one year = 90,000 × (9% + (0.4 × 0.06)) × 1.10 = 11,286; Employee after-tax contribution = 90,000 × (9% × (1 − 28%)) = 5,832; HPR = (11,286/5,832) − 1 = 93.52%

CHAPTER 15 An insurance company's projected loss ratio is 79.4 percent, and its loss adjustment expense ratio is 13.7percent. It estimates that commission payments and dividends to policyholders will add another 15 percent. What is the minimum yield on investments required in order to maintain a positive operating ratio in percent?

Combined ratio = 79.4% + 13.7% + 15% = 108.10%.In order to be profitable, the yields on investments have to be greater than 8.10%.

CHAPTER 7 You bought your house five years ago and you believe you will be in the house only about five more years before it gets too small for your family. Your original home value when you bought it was $250,000, you paid 20 percent down, and you financed closing costs equal to 3 percent of the mortgage amount. The mortgage was a 30-year fixed-rate mortgage with a 6.5 percent annual interest rate. Rates on 30-year mortgages are now at 5 percent if you pay 2 points (which you will). Your refinancing costs will be 1.5 percent of the new mortgage amount (excluding points). You have decided to pay for the points and the closing costs out of your past savings. A new down payment is not required. Should you refinance? Ignore all taxes and show your work.

Find the original payment and then find what you owe now: Step 1 PV = 206,000 I = 6.5/12 = 0.5417 N = 360 FV = 0 Solve for PMT to get 1,302.06 Step 2 Find the balance left on this loan which is 192,838.61. Step 3 The new loan will have a payment of: PV = 192,838.61 I = 5/12 = 0.4167 N = 360 FV = 0 Solve for the PMT to get 1,035.20. So the savings on monthly payments will be 1,302.06 − 1,035.20 = 266.86. The refinancing costs on the new mortgage will be 0.035 × 192,838.61 = 6,749.35. If you will leave in this house only 5 more years, find whether $6,749.35 is worth paying today. Solve for the number of years required to recover this $6,749.35 cost today: PV = − 6,749.35 I = 5/12 = 0.4167 PMT = 266.86 FV = 0 Solve for N to get 26.78 months which is equivalent to 2.23 years which is less than the 5 years period you intend to stay in the house, so it is worth refinancing.

CHAPTER 18 Congratulations, you have just been employed! You now have a choice between a flat benefit at retirement equal to $4,000 times your years of service, or a career average formula of 3.50 percent of your average salary times your years of service. You expect to work 40 years. At what average salary would you be indifferent between the two alternatives?

Flat Benefit: ($4,000 × 40) = 160,000 Average Benefit : 0.035 × 40 x n = 160,000 n=$114,286

CHAPTER 9 A U.S. FI has US$200 million worth of one-year loans earning an average rate of return of 6 percent. The FI also has one-year single-payment Canadian dollar loans of C$110 million earning 8 percent. The FI's funding source is $300 million in US$ one-year CDs, on which they are paying 4 percent. Initially the exchange rate is C$1.10 per US$1. The one-year forward rate is C$1.14 per US$1. What is the bank's dollar percent spread (in %) if they hedge fully using forwards? Show your work with correct currency name or sign,

Hedge by selling C$ forward. The current C$ amount is C$110 million. In one year these loans will be worth $110 million × 1.08 = C$118,800,000. Selling this amount forward, C$118,800,000/C$1.14 will give US$104,210,526. This gives a rate of return of [US$104,210,526/US$100 million] − 1 = 4.211%. Average rate of return = (2/3 × 6%) + (1/3 × 4.211%) = 5.404% The cost rate = 4%, so the spread = 5.404% − 4% = 1.404%

CHAPTER 18 An employee contributes 6 percent of her salary to her 401(k) plan and her employer contributes another $1,900. The employee earns $75,000 and is in a 28 percent tax bracket. If the employee earns 8.50 percent on all funds invested each year and her salary does not change, how much will she have in her account in 20 years?

Input N = 20, I = 8.5, PMT = 6,400, PV = 0 to solve for FV 309,612.88

CHAPTER 7 You plan to purchase an $120,000 house using a 30-year mortgage obtained from your local bank. The mortgage rate offered to you is 4.5 percent. You will make a down payment of 10 percent of the purchase price. A) Calculate the amount of interest and, separately, principal paid in the 250th payment. B) Calculate the amount of interest paid over the life of this mortgage.

Monthly pmt: 547.22 (PV -108,000; FV 0; I/Y 4.5/12; N 360) A) Step 1: Outstanding Loan Balance FV 0; I/Y 4.5/12; PMT 547.22; N360-249 CPT PV--> 49,610.38 Step 2: int pmt =loan balance X monthly rate 49,610.38 X (.04512) =186.04 Step 3: Principal pmt = monthly pmt - interest pmt 547.22-186.04 = 361.18 B) Total int paid = total amt of pmt - borrowed amt (547.22 x 360) - 108,000 = 196999.2 - 108,000 =88,999.2

CHAPTER 15 You deposit $14,000 annually into a life insurance fund for the next 10 years, after which time you plan to retire. If the deposits are made at the beginning of the year and earn an interest rate of 7 percent, what will be the amount in the retirement fund at the end of year 10?

N = 10 PMT = 14,000 PV= 0 I/Y = 7% BEG CPT FV = 206,970.39

CHAPTER 15 An insurance line has a loss ratio of 62 percent and an expense ratio of 35 percent; the firm pays 2 percent of premiums to policyholders as dividends and has an investment yield to premium ratio of 9 percent. The operating ratio for this line is

Operating ratio = 62 + 35 + 2 - 9 = 90

CHAPTER 15 You have a policy with a cash value of $250,000 which you wish to annuitize. You are currently 62 years old (life expectancy 14 years) and your spouse is 58. Your spouse is expected to outlive you by 8 years. Interest rates are 5% per year, and you are considering receiving monthly payments under two options. With option 1 you will receive a monthly payment until you die. With option 2 you will receive a monthly payment until both you and your spouse die. How much will you receive per month with each option (ignoring administrative costs and fees)?

Option 1) PV = 250,000; I/Y = 5/12; FV=0; N=14 x 12=168 CPT PMT= 2,072.17 Option 2) PV = 250,000; I/Y = 5/12; FV=0; N=22 x 12=264 CPT PMT= 1,563.20

CHAPTER 15 What is the amount of the annuity purchase required if you wish to receive a fixed payment of $240,000 for 20 years? Assume that the annuity will earn 10 percent per year.

PMT = 240,000 N = 20 I/Y = 10% FV = 0 CPT PV = $2,043,255.29

CHAPTER 15 Calculate the annual cash flows from a fixed-payment annuity if the present value of the 20-year annuity is $1.4 million and the annuity earns a guaranteed annual return of 10 percent. The payments are to begin at the end of the current year.

PV = 1,400,000 FV = 0 N = 20 I/Y = 10% END CPT PMT =$164,443.47

CHAPTER 15 An insurance company collected $4.4 million in premiums and disbursed $2.14 million in losses. Loss adjustment expenses amounted to 7 percent and dividends paid to policyholders totaled 1.2 percent. The total income generated from their investments was $200,000 after all expenses were paid. What is the net profitability in dollars?

Premiums 4,400,000 Losses 2,140,000 LAE 7% x 4,400,000 = 308,000 Dividend 1.2% x 4,400,000 = 52,800 Investment Income = 200,000 Net Profitability = 4,400,000 - 2,140,000 - 308,000 - 52,800 + 200,000 = $2,099,200

CHAPTER 7 You plan to purchase a house for $118,000 using a 15-year mortgage obtained from your local bank. You will make a down payment of 10 percent of the purchase price. You will not pay off the mortgage early. Assume the homeowner will remain in the house for the full term and ignore taxes in your analysis. Your bank offers you the following two options for payment: Option 1: Mortgage rate of 5 percent and zero points. Option 2: Mortgage rate of 4.85 percent and 1.0 points. Which option should you choose? Show detailed calculation in support of your choice.

Step 1: Monthly Pmts Option 1: 839.82 N:180 PV:-106,200 I/Y:5/12 FV:0 Option 2: 831.55 N:180 PV:-106,200 I/Y:4.85/12 FV:0 Step 2: PV of Savings Savings=839.82 - 831.55 = 8.27 (PMT) N:180 PMT:8.27 I/Y:4.85/12 FV:0 CPT PV: 1056.19 Savings Amt 1056.19 < Price of that savings 1062 (106200 x 1%) Therefore, you should choose option 1.

CHAPTER 2 Based on economists' forecasts and analysis, one-year T-bill rates and liquidity premiums for the next four years are expected to be as follows:1R1 = .32%E(2r1) = .68% L2 = 0.05%E(3r1) = .78% L3 = 0.16%E(4r1) = 1.08% L4 = 0.18% Identify the four annual rates for Years, 1, 2,3 and 4.

Year 1: 0.32% Year 2: [(1 + .0032)(1 + .0068 + .0005)]^(1/2) - 1 = 0.52% Year 3: [(1 + .0032)(1 + .0068 + .0005)(1 + .0078 + .0016)]^(1/3) - 1 = 0.66% Year 4: [(1 + .0032)(1 + .0068 + .0005)(1 + .0078 + .0016)(1 + .0108 + .0018)]^(1/4) - 1 = 0.81%

CHAPTER 2 You are considering an investment in 30-year bonds issued by Moore Corporation. The bonds have no special covenants. The Wall Street Journal reports that one-year T-bills are currently earning 0.40 percent. Your broker has determined the following information about economic activity and Moore Corporation bonds: Real risk-free rate = 0.35% Default risk premium = 1.15% Liquidity risk premium = 0.70% Maturity risk premium = 0.95% a. What is the inflation premium? b. What is the fair interest rate on Moore Corporation's 30-year bonds?

a) T-bill - RFR =inflation premium0.40% - 0.35% = 0.05% b) i = IP + RFR + DRP + LRP + SCP + MP= 0.05% + 0.35% + 1.15% + 0.70% + 0% + 0.95%=3.20%

CHAPTER 2 A particular security's equilibrium rate of return is 9 percent. For all securities, the inflation risk premium is 2.95 percent and the real risk-free rate is 2.8 percent. The security's liquidity risk premium is 0.65 percent and maturity risk premium is 0.95 percent. The security has no special covenants. Calculate the security's default risk premium. Calculate default risk premium:

i = IP + RFR + DRP + LRP + SCP + MP 9% = 2.95% + 2.8% + DRP + 0.65% + 0% + 0.95% 9% = 7.35% + DRP 9% - 7.35% = DRP 1.65% = DRP

CHAPTER 15 A property-casualty insurer brings in $6.22million in premiums on its homeowners MP line of insurance. The line's losses amount to $4,304,240, expenses are $1,567,440, and dividends are $136,840. The insurer earns $199,040 in the investment of its premiums. Calculate the line's loss ratio, expense ratio, dividend ratio, combined ratio (after dividends), investment ratio, operating ratio, and overall profitability

loss ratio = 4,304,240/6,220,000 = 69.2 % expense ratio = 1,567,440/6,220,000 = 25.2% dividend ratio = 136,840/6,220,000 = 2.2% combined ratio after dividends = 69.2 + 25.2 + 2.2 = 96.6% investment ratio = 199,040/6,220,000 = 3.2% operating ratio = 96.6 - 3.2 = 93.4% overall profitability = 100 - 93.4 = 6.6%