FNFP Finance Class
Suppose a bond will pay $1,000 in 2 years. At the end of the next 2 years, the bond will pay a coupon of $50. Assume a discount rate of 5%. What is the price of this bond?
$1,000
Suppose a bond will pay $1,000 in 2 years. At the end of each of the next 2 years, the bond will also pay a coupon of $50. Assume a discount rate of 3%. What is the price of this bond?
$1,038.27 $1,000/(1+3%)^2 +$50/(1+3%)^2 +$50/(1+3%)
Suppose a bank pays an annual interest rate of 5% compounded annually. The account holder's initial investment was $1,000. How much should the account holder expect to be in the bank after 5 years?
$1,276.28
Suppose a project requires an initial investment of $2.8 million. This initial investment is to be depreciated straight-line to 0 in 4 years. It generates an annual sales of $2,360,000, with annual costs of $520,000. Assume a tax rate of 35%. What is the annual operating cash flow from this project?
$1,441,000 2360000 - 520000 - 644,000 + 245000 = 1,441,000
Choose between these prizes if the interest rate is 10%: $1,000 now or $1,500 at the end of 4 years.
$1,500 at the end of 4 years. PV of $1,500 in 4 years at 10% interest = FV/(1+r)^t = $1,500/(1+10%)^4 = $1,025
Suppose you put $1,000 into a bank account that pays an annual nominal interest rate of 5%. What will be the account balance at the end of 10 years? Assume there is no deposit or withdrawal in the interim.
$1,628.90 $1,000*(1+5%)^{10} = $1,628.90
Suppose you put $1,000 into a bank account that pays an annual nominal interest rate of 5%. What would the account balance be at the end of 10 years if the interest rate is compounded semi-annually at 1/2 the annual nominal rate?
$1,638.62 $1,000*(1+5%/2)^{(2*10)} = $1,638.62
Suppose you put $1,000 into a bank account with an annual nominal interest rate of 5%. What will be the account balance at the end of 10 years if the interest is compounded quarterly at 1/4 the annual nominal rate?
$1,644 $1,000*(1+5%/4)^(10*4) = $1,644
Suppose you put $1,000 into a bank account with an annual nominal interest rate of 5%. What will be the account balance at the end of 10 years if the interest is compounded daily at 1/365 the annual nominal rate?
$1,649 $1,000*(1+5%/365)^(10*365) = $1,649
Suppose company XYZ has revenues of $500 million, cost of goods sold of $300 million, and depreciation of $100 million. What is the company's EBIT?
$100 million $500-$300-$100 = $100
Suppose company XYZ has revenues of $500 million, cost of goods sold of $300 million, and depreciation of $100 million. It also pays a 30% tax and has, in addition, an increase in net working capital of $50 million, and capital expenditure of $10 million. What is XYZ's FCF?
$110 million 70 (NOPAT) + 100 (Dep) - 50 (NWC) -10 (CAPEX) = 110
Suppose the bank pays an annual interest rate of 5% compounded annually, and the interest every year is distributed to the account holder (not compounded). What would the account balance be in 5 years if the initial investment was $1,000?
$1250
A company has operating income of $100 million, depreciation of $5 million, an asset sale of $50 million, a CapX of $10 million, and an increase in net working capital of $10 million. Calculate this company's FCF for the year.
$135 million $100 + $5 + $50 - $10 -$10 = $135
A company has an operating income of $100 million, no depreciation, an asset sale of $50 million, a capital expenditure of $10 million, and no changes in net working capital. Calculate this company's free cash flow for the year.
$140 million $100 + $50 - $10 = $140
If Ann offered Ben $175 payable 5 years from now, how much would Ben pay for that offer today if interest rates were 4%?
$143.84
A company has an operating income of $100 million, depreciation of $5 million, an asset sale of $50 million, and a capital expenditure of $10 million. Calculate this company's FCF for the year.
$145 million. $100 + $5 + $50 - $10 = $145
A company has operating income of $100 million, depreciation of $5 million, an asset sale of $50 million, a CapX of $10 million, and a decrease in net working capital of $10 million. Calculate this company's FCF for the year.
$155 million $100 + $5 + $50 - $10 +$10 = $155
Suppose an investment requires an initial investment of $1.4 million. This initial investment is to be depreciated straight-line to 0 in 3 years. It generates an annual sales of $1,120,000, with annual costs of $480,000. Assume a tax rate of 35%. What would be the tax savings from depreciation?
$163,333.33 0.35*466,666.67 = $163,333.33
Suppose you put $1,000 into a bank account with an annual nominal interest rate of 5%. What will be the account balance at the end of 10 years if the interest is compounded monthly at a rate of 1/12 the nominal rate.
$1647 $1,000*(1+5%/12)^(10*12) = $1,647
$1,000 was deposited into a bank account with an 11% annual interest rate. How much would be in that bank account after 5 years?
$1685
If you need $20,000 for a car purchase by the time you graduate from college in 4 years and annual nominal interest rates are 2%, how much would you need to put into savings today?
$18,476.91 PV = FV/(1+r)^t = $20,000/(1+2%)^4
What is the present value of a simple bond with face value of $2,000 that makes annual payments of $200 for 3 years at a discount rate of 5%?
$2,272.33 PV in year 1 = FV/(1+r)^t = ($200)/(1.05)^1 = $190.48 PV in year 2 = ($200)/(1.05)^2 = $181.41 PV in year 3 = ($2,000 + $200)/(1.05)^3 = $1,900.44 PV of bond = sum of all cash flows = $2,272.33
What is the value of a share of stock in Company A that is earning $1.57 per share using a P/E ratio valuation to comparable Company B trading at $15 and a P/E ratio of 14 with earnings of $2.42 per share?
$21.98 Value of Company A = P/E of Company B * Earnings of Company A = 14 * $1.57 = $21.98
Suppose an investment requires an initial investment of $1.4 million. This initial investment is to be depreciated straight-line to 0 in 3 years. It generates an annual sales of $1,120,000, with annual costs of $480,000. Assume a tax rate of 35%. What is the tax to be paid on annual sales?
$224,000 (1120000-480000)*0.35 = 224,000
A company has an operating income of $200 million, no depreciation, an asset sale of $75 million, a capital expenditure of $30 million, and no changes in net working capital. Calculate this company's free cash flow for the year.
$245 million 200+75-30 = 245
Suppose a project requires an initial investment of $2.8 million. This initial investment is to be depreciated straight-line to 0 in 4 years. It generates an annual sales of $2,360,000, with annual costs of $520,000. Assume a tax rate of 35%. What would be the tax savings from depreciation?
$245,000 0.35*700000 = 245,000
Suppose Company XYZ has revenues of $700 million, cost of goods sold of $200 million, and depreciation of $50 million. It also pays a 25% tax. In addition, it has an increase in net working capital of $80 million, and capital expenditure of $30 million. What is XYZ's FCF?
$277.5 million 337.5 (NOPAT) + 50 (Dep) - 80 (NWC) -30 (CAPEX) = 277.5
There's a $3,000 Bond that makes annual payments of $250 for 5 years. Year 5 is bond maturity. If the discount rate is 7%, what is it worth?
$3,164
If the annual nominal interest rate is 15%, would you rather have $800 now or $3,500 at the end of 10 years?
$3,500 at the end of 10 years. PV=FV/(1+r)^t = 3,500/(1+0.15)^10 = $865
Suppose Company XYZ has revenues of $700 million, cost of goods sold of $200 million, and depreciation of $50 million. It also pays a 25% tax. What would be the company's NOPAT?
$337.5 million 450*(1-25%) = 337.5
Assume an investment costing $24,869 will earn $10,000 a year for ten years. If the discount rate is 10%, what is the NPV of this project?
$36,577 -24869+(10000/0.1)*(1-(1/1.1^{10})) = $36,577
What is the NPV of a project that requires an initial outlay of $1000 and provides an annual outcome of $500 for 3 years? Assume a Discount Rate of 5%, and each annual income is paid at the end of each year.
$361.62
What is the value of a a bond with a face value of $4,000 that makes annual payments of $500 for 3 years at an annual discount rate of 6%?
$4,695 PV = FV/(1+r)^t = ($500)/(1.06)^1 + ($500)/(1.06)^2 + ($4,500)/(1.06)^3 = $4,695
Suppose Company XYZ has revenues of $700 million, cost of goods sold of $200 million, and depreciation of $50 million. What is the company's EBIT?
$450 million $700-200-50 = $450
A project requires an initial investment of $1.4 million. This initial investment is to be depreciated straight-line to 0 in 3 years. What is the annual depreciation amount?
$466,666.67 $1.4M/3 = $0.467M
Suppose an investment requires an initial investment of $1.4 million. This initial investment is to be depreciated straight-line to 0 in 3 years. It generates an annual sales of $1,120,000, with annual costs of $480,000. Assume a tax rate of 35%. What is the annual operating cash flow of this project?
$579,333.33 1120000 - 480000 - 224,000 + 163,333.33 = 579,333.33
What is the present value of a simple bond with a face value of $6,000 and makes annual payments of $300 for 5 years at a discount rate of 3%?
$6,549.56 PV in year 1 = FV/(1+r)^t = $300/(1.03)^1 = $291.26 PV in year 2 = $300/(1.03)^2 = $282.78 PV in year 3 = $300/(1.03)^3 = $274.54 PV in year 4 = $300/(1.03)^4 = $266.55 PV in year 5 = ($6,000 + $300)/(1.03)^5 = $5,434.44 PV of bond = sum of all cash flows = $6,549.56
Suppose a project requires an initial investment of $2.8 million. This initial investment is to be depreciated straight-line to 0 in 4 years. It generates an annual sales of $2,360,000, with annual costs of $520,000. Assume a tax rate of 35%. What is the tax to be paid on annual sales?
$644,000 (2360000-520000)*0.35 = 644,000
Suppose company XYZ has revenues of $500 million, cost of goods sold of $300 million, and depreciation of $100 million. It also pays a 30% tax. What would be the company's NOPAT?
$70 million 100*(1-30%) = 70
A project requires an initial investment of $2.8 million. This initial investment is to be depreciated straight-line to 0 in 4 years. What is the annual depreciation amount?
$700,000 $2.8M / 4 = $ 0.7M
A pizza parlor owner wants a friend to pay him today to open his business. The pizza parlor owner promises he'll pay his friend $1000 in 7 years with a 5% interest rate. At that rate and over that amount of time, how much will his friend loan him today?
$710.70
Ben has a loan of $1,000 that is due 5 years from now (due at the end of year 5). Suppose a bank account pays an annual interest rate of 5%. How much would Ben have to put into this account today in order to be able to pay off the loan in 5 years?
$783.53
Suppose a bond will pay $1,000 in 2 years. At the end of each of the next 2 years, the bond will also pay a coupon of $50. Assume a discount rate of 10%. What is the price of this bond?
$913.22 $1,000/(1+10%)^2 +$50/(1+10%)^2 +$50/(1+10%)
A project requires an initial investment of $750,000 depreciated straight-line to $0 in 4 years. The investment is expected to generate annual sales of $400,000 with annual costs of $120,000 for 4 years. Assume a tax rate of 30% and a discount rate of 14%. What is the NPV of the project?
-$15,016 FCF = (400,000-120,000-750,000/4)*(1-0.3) + (750,000/4) = 252,250 NPV = -750,000 + 252,250/1.14 + 252,250/1.14^2 + 252,250/1.14^3 + 252,250/1.14^4 = -15,016
A project requires an initial investment of $1.4 million depreciated straight-line to $0 in 3 years. The investment is expected to generate annual sales of $1,120,000 with annual costs of $480,000 for 3 years. Assume a tax rate of 35% and a discount rate of 12%. What is the NPV of the project?
-$8,539.09 FCF=($1,120,000 - $480,000 - $1,400,000/3)*(1-0.35)+(1,400,000/3) = $579,333.33 NVP=(-$1,400,000 + $579,333.33/(1+0.12)^1 + $579,333.33/(1+0.12)^2 + $579,333.33/(1+0.12)^3 = -$8,539.09
A stock has an expected return of 10.2%, the risk-free rate is 4%, and the market risk premium is 7%. What must be the beta of this stock?
0.89 0.102=0.04+0.07*beta => beta = 0.89
What is the beta of the market portfolio?
1
A stock has an expected return of 15.3%, the risk-free rate is 5%, and the market risk premium is 8%. What must be the beta of this stock?
1.29 0.153=0.05+0.08*beta => beta = 1.29
If a stock has a beta of 1.8, equity premium of 5.5% and the risk free rate is 3%, what is the cost of equity (or Re)?
12.9% Re = (1.8*5.5)+3
What is the ROI of a project that requires investments of $500 in each of the first 3 years, and yields an income of $100, $75, and $50 in each of the first 3 years?
15% (average investment/average income)
The total market value of the company stock of XYZ Real Estate Company is $6 million, and the total value of its debt is $4 million. The treasurer estimates that the beta of the stock is currently 1.5 and that the expected risk premium on the market is 9%. The Treasury bill rate is 8%. Assume the company's cost of debt equals the risk free rate. Estimate the company's cost of capital.
16.1% Re = 0.08 + (1.5)(0.9) = 21.5% WACC = (E/V)(Re) + (D/V)(Rd) = (6/10)(21.5%) + (4/10)(8%) = 16.1%
Company XYZ has a beta of 1.4. Assume the Treasury bond rate is 6%, and the risk premium is 8.5%. What is the expected return on XYZ's stock?
17.9% 6%+1.4*8.5%=17.9%
Suppose XYZ Real Estate Company now wants to produce computers. The average beta of unlevered computer manufacturers is 1.2. Estimate the required return on XYZ's new venture.
18.8% Re = 1.2*(1+*4/6) = 26% WACC = (E/V)(Re) + (D/V)(Rd) = (6/10)(26%) + (4/10)(8%) = 18.8%
A project requires an initial investment of $2000 upfront. It will produce an annual income of $1000 every 3 years. When is this project's payback period, without considering discounting?
2 years
A project requires an initial investment of $2000 upfront. It will produce an annual income of $1000 every year for 3 years. Assume a discount rate of 10%. What is the payback period (discounted) for the above project?
2.352 To Solve (After getting PV[CF]): 1. $2000 - PV[CF1] - PV[CF2] = Remaining Balance 2. Remaining Balance/(PV[CF3]) = Remainder or Absolute Value | (Initial Investment + PV[CF] + PV[CF]...)/Final PV[CF]. Add that remainder to last round period for final answer.
Company XYZ has a beta of 1.5. Assume the Treasury bond rate is 7%, and the risk premium is 9.5%. What is the expected return on XYZ's stock?
21.25% 7%+1.5*9.5%=21.25%
A company has 25% of its assets financed by debt. What is this company's debt-equity ratio?
33.3% 25% debt => 75% equity. 25%/75% = 33.3%
The equity value of Target is $40Billion. They have roughly 15B in long-term debt They pay a 35% corporate tax rate. Their beta is 0.6 Assume treasury rates are 2.5% and the equity premium is 5.5% They're A-rated with a quality spread of 120 bps. Estimate Target's WACC.
4.87% WACC = (40/(40+15))(2.5% + (0.6)(5.5%)) + (15/(40+15))(1-35%)(2.5%+1.20%) = 4.87%
Company ABC has a WACC of 11.2%, a cost of equity of 14%, and a cost of debt of 5%. What is ABC's debt-equity ratio?
45% 11.2%=14%*E/V + 5%*(1-E/V) E/V = 69% => D/V = 31% => D/E = 31/69 = 45%
What is the historically consistent range for Risk Free Rate?
5-7%
A company has 35% of its assets financed by debt. What is this company's debt-equity ratio?
53.8% 35% debt => 65% equity D/E ratio 35%/65% = 53.8%
Suppose the risk-free rate is 5%; on average a AAA-rated corporate bond carries a credit spread of 0.1%, an A-rated corporate bond carries a credit spread of 1%, and a B-rated corporate bond carries credit spread of 3%. Company XYZ's outstanding debt is rated A by ratings agencies. What would be the cost of debt for XYZ based on prevailing market rates?
6% (5% +1% = 6%)
A nominal rate of 6% compounded monthly is what, effectively?
6.17%
Company XYZ has a target capital structure of 50% equity and 50% debt. Its cost of capital is 10% and cost of debt is 5%. What is XYZ's WACC with a tax rate of 30%?
6.75% WACC= (50/50+50)(10%) + (50/50+50)(1-30%)(5%) = 7.5%
A company has a debt-equity ratio of 50%. How much of this company's assets are financed by equity?
66.6% D/E is 50% => E/(D+E) = 66.6%
Over the years 2051 - 2060, the average annual return on the overall stock market is 10%, and the average risk-free rate is 3%. What is the stock market risk premium during those 10 years?
7% (10%-3%)
If you invest $1,000 in a bank paying an annual nominal interest rate of 10% compounded annually, how long would it take to double the initial investment?
7.27 years. FV/PV = (1+r)^t 2=(1+10%)^t log(2) = log((1+10%)^t) 7.27 = t
Company XYZ has a target capital structure of 50% equity and 50% debt. Its cost of equity (Re) is 10% and cost of debt (Rd) is 5%. What is XYZ's weighted average cost of capital (WACC)? Suppose there is no tax.
7.5% WACC= (50/50+50)(10%) + (50/50+50)(1-0)(5%) = 7.5%
A company has a debt-equity ratio of 40%. How much of this company's assets are financed by equity?
71.4% D/E = 40% = 40/100 => D = 40, E =100 E/(D+E) = 100/140 = 71.4%
What is the IRR of a project that requires an initial outlay of $15,200, and inflows of $5,000, $6,000, and $7,000, each at the end of the first 3 years?
8.38%
Company FIN has a WACC of 9.8%, a cost of equity of 13%, and a cost of debt of 6.5%. What is FIN's debt-equity ratio?
97% 9.8%=13%*E/V + 6.5%*(1-E/V) => E/V = 50.77% => D/E = 97%
Why, empirically, does a AAA-rated bond carry a lower yield compared to a B-rated bond?
A AAA-rated bond carries less risk
An increase in net working capital means
A decrease in cash. Increases in net working capital represents a net drain of cash from the firm.
How does an increase in current liabilities affect cash? A. Increases cash B. Decreases cash C. No effect on cash
A. Increase Cash. An increase in current liabilities represents an increase in cash which the firm owes within 1 year.
An initial investment of $20,000 has a cash inflow of $50,000 in year 1 and a cash outflow of $10,000 in year 2. The firm has a cost of capital of 15%. Calculate the IRR for this project. Should the firm accept or reject the project?
Accept. -20,000 + (50,000/(1+IRR)^1 ) - (10,000/(1+IRR)^2) = 0 Solving for IRR => -78%, 128% Since only non-negative discount rates are possible, IRR = 128% Since the firm's cost of capital is below 128%, the firm should take the project.
To get Free Cash Flows from accounting earnings, do I add back depreciation and amortization and subtract capital expenditures, or do I subtract depreciation and amortization and add back capital expenditures?
Add back depreciation and amortization and subtract capital expenditures. D&A is not a cash expense so it is added back to get to FCF. CapX is a cash expense not included in accounting earnings so it's subtracted to get FCF.
In the Capital Budgeting Process of deciding how to spend the cash generated by the firm, the financial manager can: -Pay Dividends -Reinvest -Pay Off Debt -All of the Above
All of the Above (cash generated by the firm can be used to pay equity lenders, debt holders, and/or reinvest in projects within the firm.
What is the correct accounting identity: Equity=Assets + Debt Debt=Equity+Assets Assets=Debt+Equity
Assets=Debt+Equity
What are the 3 main financial statements used to communicate the financial results of the firm to outside investors?
Balance Sheet, Income Statement, Cash Flow Statement
What is a measure of an asset's riskiness?
Beta
What is Beta?
Beta measures how much a stock moves relative to the overall market and represents the riskiness of the asset.
What is net working capital? Shareholders equity less assets, current assets minus current liabilities, or debt less assets?
Current assets minus current liabilities. Working capital represents money that is owed to or owed from the firm within the next year that has not yet come in or out as cash, such as money invested in inventory which has not yet been sold and money which has not yet been received from customers for goods received.
Historically, which one of the following has provided the highest risk premium? A. T-Bills B. Treasury Bonds C. AAA Corporate Bonds D. Stock Market Index
D. Stock Market Index
A water well in the desert produces 1 gallon of water per day resulting in net cash flow of $1.50 per day. If I have less confidence in the ability to earn $1.50 per day in cash flow from this water well, will I discount the investment more or less, and will this increase or decrease the present value of the asset?
Discount more, decrease Present Value
True or False: Comps provide practitioners a more accurate value of an assets value than the value provided by DCF.
False - comparable transactions are a simplified method of valuation commonly used by practitioners and is highly dependent on identifying a comparable asset.
In evaluating a project, depreciation is considered as a method of discounting cash flows. True or False.
False - depreciation accounts for the declining book value of the assets which become worth less in time.
The price of stock market risk, or the equity premium, is around 10-12%. True or False?
False - the Stock Market has historically returned an average 10-12% but the equity premium is the additional risk taken on in the stock market over the risk free rate, and is around 5.5%
Accounting earnings or bottom-line net income is an accurate representation of the cash creation of the firm. True or False?
False. Accounting earnings must incorporate write-downs for things such as depreciating assets that are not reflective of cash creation for the firm in that period.
Discounted Cash Flow values an investment by estimating the cash flow in the final period and discounting this value to the present. True or False?
False. Discounted Cash Flow considers all cash flows throughout the life of the investment, not just the cash flow in the final period.
As a metric for free cash flows of the firm, EBITDA is the revenue less the COGS, Sales General & Administrative costs, depreciation, interest, and taxes. True or False?
False. EBITDA is a metric for free cash flows generated by the operations of the firm, independent of tax rate and the levels of debt within the firm. Therefore EBITDA is pulled from the accounting statement prior to depreciation, interest, and tax expense.
If the NPV of a project is <0, it is a profitable investment for the firm. True or False.
False. In NPV, the initial investment is subtracted from all future cash flows; therefore, a negative NPV is not a profitable investment.
A water well in the desert produces 1 gallon of water per day resulting in net cash flow of $1.50 per day. To calculate the present value of the water well, multiply $1.50 per day by some practical number of days. True or false?
False. The future cash flows must be discounted to get to the present.
The safest place to invest your money is the bank since it is backed by the FDIC. True or False?
False. U.S. Treasuries are backed by the U.S. government and represent the lowest risk for investing your money
True or False: Greater risk decreases the amount of money I require to wait.
False: If I take on greater risk by waiting, I require more compensation for waiting.
Firm A has a debt-equity ratio of 100%, whereas firm B has a debt-equity ratio of 10%. Suppose A and B are identical in all other aspects. Which one should have a higher beta?
Firm A. Firm A has higher financial leverage, and therefore should be more risky.
Assuming everything else remains the same in the prior question, what would happen to the IRR if the initial investment increases from $1,000 to $1,050?
IRR Decreases
You are evaluating an investment that requires $1,000 upfront, and pays $50 at the end of each of the first 2 years, and an additional lump-sum of $1,000 at the end of year 2. What would happen to the IRR if the annual payments at the end of each of the first 2 years go down from $50 to $40?
IRR Decreases
You are evaluating an investment that requires $5,000 upfront and pays $80 at the end of each of the first 4 years and an additional lump-sum of $12,000 at the end of year 4. What would happen to the IRR if the annual payments at the end of each of the first 4 years go up from $80 to $90?
IRR Increases
You are evaluating an investment that requires $5,000 upfront and pays $80 at the end of each of the first 4 years and an additional lump-sum of $12,000 at the end of year 4. What would happen to the IRR if the initial investment decreases from $5,000 to $4,000?
IRR Increases
The firm sells a piece of equipment no longer needed for operation. This asset has a book value of $1000. What impact does this sale have on FCF? Does it increase, decrease, or have no impact on FCF?
Increases FCF. The Salvage Value of an asset increases FCF.
A water well in the desert produces 1 gallon of water per day resulting in net cash flow of $1.50 per day. Will the present value of the cash flows in year 20 be more or less than the cash flow from the water well in year 2?
Less. Due to the effect of discounting cash flow further out in the future is exponentially less valuable today.
Machine A costs $5,000 and depreciates on a 4-year schedule. Machine B costs $4,000 and depreciates on a 5-year schedule. Which machine has a higher Net Fixed Asset value on the Balance Sheet in year 1?
Machine A Machine A = $5,000-($5,000/4) = $3,750 Machine B = $4,000-($4,000/5) = $3,200
A piece of equipment costs $1500, if this asset depreciates on a 5 year schedule, the Net Fixed Asset value on the Balance Sheet in year 1 will be more or less than this same asset depreciating on a 3 year schedule?
More. Net Fixed Asset on 5-year depreciation: $1500 - ($1500/5) = $1200 Net Fixed Asset on 3-year depreciation: $1500 - ($1500/3) = $1000
What would happen to a project's NPV if its cash inflows are pushed further into the future?
NPV Decreases
What would happen to a project's NPV with an increase in initial investment?
NPV Decreases
What would happen to a project's NPV if the estimated cash inflows are expected sooner?
NPV Increases
What would happen to a project's NPV with a decrease in initial investment?
NPV would increase
Company XYZ has a target capital structure of 50% equity and 50% debt. Its cost of equity is 10%, and cost of debt is 5%. Suppose there is no tax. Should the company take on a project that demands an initial investment of $500 million, and provides an income of $600 million in 3 years?
No 600/(1+7.5%)^3 3 = 482.98 < 500
Company XYZ has a target capital structure of 60% equity and 40% debt. Its cost of equity is 12%, and cost of debt is 6%. Suppose there is no tax. Should the company take on a project that demands an initial investment of $600 million, and provides an income of $800 million in 4 years?
No. WACC = (E/V)(Re) + (D/V)(Rd) = (6/10)(12%) + (4/10)(6%) = 9.6% 800/(1+9.6%)^4 = 554 < 600
An initial investment of $1,500 has cash flows of $900 in year 1 and $750 in year 2. Using NPV, do you invest in this project with a discount rate of 10%?
No. -1500+(900/1.1) + (750/1.1^2) = -62 => NPV less than zero, don't do project
Company XYZ is considering an investment that requires an initial outlay of $500 million, and yields an income of $505 million one year from now. Should this project be accepted if the company requires a discount rate of 10%?
No. 505/(1+10%)^1 < $500
What are the 3 main factors that affect interest rates?
Opportunity costs, inflation, risk
What happens to the present value of $1,000 when the due date that it is to be paid changes from 5 years to 4 years? Does the PV go up or down?
PV goes up. Decreasing t in the formula PV = FV/(1+r)^t slams down the PV less.
Project A requires an initial outlay of $1,000 and provides an annual income of $500 for 3 years. Project B requires an initial outlay of $2,000 and yields an annual income of $900 for 3 years. Compare the two projects described directly above. Which one would you pick based on their payback periods?
Project A Project A has a payback period of 1000/500=2 years, whereas Project B has a payback period of 2000/900=2.22 years.
Which project would you select based on NPVs assuming the same 5% discount rate for both? Project A requires an initial outlay of $1,000 and provides an annual income of $500 for 3 years. Project B requires an initial outlay of $2,000 and yields an annual income of $900 for 3 years.
Project B Project A NPV = 500/(1+5%) + 500/(1+5%)^2 + 500/(1+5%)^3 -1000=361.62 Project B NPV = 900/(1+5%) + 900/(1+5%)^2 + 900/(1+5%)^3 - 2000 = 450.92
Project A requires an initial outlay of $500 and provides an annual income of $600 for 3 years. Project B requires an initial outlay of $400 and yields an annual income of $700 for 3 years. Compare the two projects described directly above at a discount rate of 7%. Which one would you pick based on their payback periods?
Project B Project A has a payback period of 500/600 = 0.83 years (10 months) Project B has a payback period of 400/700 = 0.57 years (7 months)
Which project would you select based on NPVs assuming the same 7% discount rate for both? Project A requires an initial outlay of $500 and provides an annual income of $600 for 3 years. Project B requires an initial outlay of $400 and yields an annual income of $700 for 3 years.
Project B Project A NPV = 600/(1+7%) + 600/(1+7%)^2 + 600/(1+7%)^3 -500 = 1,075 Project B NPV = 700/(1+7%) + 700/(1+7%)^2 + 700/(1+7%)^3 -400 = 1,437
You are using ROI to evaluate a project that requires investments of $500 in each of the first 3 years, and yields annual income of $100, $75, and $50 in each of the first 3 years. What would happen to ROI if the annual incomes double?
ROI Doubles
You are using ROI to evaluate a project that requires investments of $800 in each of the first 4 years, and yields annual income of $200, $150, $100, and $75 in each of the first 4 years. What would happen to ROI if the annual incomes are halved?
ROI Halves
Stock A has a beta of 0.8, whereas stock B has a beta of 1.5. Which one of these stocks would you recommend to a very risk-averse investor?
Stock A
Stock A has a beta of 0.8, whereas Stock B has a beta of 1.5. Which of the two stocks would you expect to provide a higher return?
Stock B (Beta is a direct measure of risk. Higher risk = higher return)
Company XYZ has a target capital structure of 50% equity and 50% debt. Its cost of equity (Re) is 10% and cost of debt (Rd) is 5%. What would happen to XYS's WAAC if its capital structure were to shift to 75% equity and 25% debt? Would it increase, decrease, or stay the same?
The WAAC would increase. A shift to put more weight on equity raises WAAC in this example, because the cost of equity is higher.
What would happen to the present value of $1000 that is to be paid in 5 years after an increase in the discount rate? Will the present value increase or decrease? Why?
The present value will decrease because a rate increase will increase the denominator in the present value discounting formula. Increasing rate and time decreases the present value, and vice versa.
Increasing the debt off of the firm decreases the cash taxes owed. True or false?
True. Debt creates a tax shield because interest expense is subtracted from pre-tax earnings, lowering actual cash taxes owed
Interest expense provides a tax shield for the firm. Is this statement true or false?
True. Interest expense is deducted from earnings before the tax rate is applied.
The availability of physical assets within a firm is a factor in evaluating the riskiness of the firm's assets. True or False?
True. They represent collateral that could be sold in the event of firm default
What happens to a firm's WACC if the firm's tax rate increases?
WACC Decreases An increase in tax rate effectively decreases the cost of debt, decreasing WACC.
Company XYZ has a target capital structure of 50% equity and 50% debt. Its cost of equity is 10%, and cost of debt is 5%. Suppose there is no tax. Should the company take on a project that demands an initial investment of $500 million, and provides an income of $600 million in 2 years?
Yes 600/(1+7.5%)^2 = 519.20 > 500
Company XYZ has a target capital structure of 60% equity and 40% debt. Its cost of equity is 12%, and cost of debt is 6%. Suppose there is no tax. Should the company take on a project that demands an initial investment of $600 million, and provides an income of $800 million in 2 years?
Yes WACC = (E/V)(Re) + (D/V)(Rd) = (6/10)(12%) + (4/10)(6%) = 9.6% 800/(1+9.6%)^2 = 666 > 600
A bond with a face value of $10,000 that makes annual payments of $200 for 5 years at a discount rate of 3% is being offered for $9,000 today. Is this a profitable bond?
Yes. PV = FV/(1+r)^t = ($200)/(1.03)^1 + ($200)/(1.03)^2 + ($200)/(1.03)^3 + ($200)/(1.03)^4 + ($10,200)/(1.03)^5 = $9,542.03
Company A is earning $2.46 per share and currently trading at $10 per share. Comparable Company B is trading at $24 per share and a P/E ratio of 4.6. Using a P/E ratio valuation, would you buy shares in Company A?
Yes. If we use the PE ratio of Company B to value Company A, then: Company A = P/E of Company B * Earnings of Company A = 4.6 * $2.46 = $11.32 This implies that Company A is worth $11.32 per share. Since it is only trading at $10, you should buy the stock!
If the annual nominal interest rate is 15%, would you rather have $800 now, $3,500 at the end of 10 years, compounded quarterly, or $3500 at the end of 10 years, compounded daily?
You would rather have $3,500 at the end of 10 years compounded quarterly. Convert nominal rate to effective rate (use 4 for quarterly, 365 for daily): Effective = ((1 + nominal/4)^4)-1 Effective Rate=15.87%, use this for r or simply: PV=FV/(1+r)^t = $3,500/(1+15/4%)^10*4=$803