Free practice final
Corporate Finance practice final (free, with answers)
A typical intro corporate finance final is mostly calculation: present and future values, annuities and loan payments, NPV, IRR and payback, bond and stock prices, expected return and the CAPM, and the weighted average cost of capital, plus a few concept questions on risk and capital structure. Have a financial calculator or spreadsheet ready, work each problem before you open the answer, and check that your timing and compounding assumptions match the question.
Topics
- Time Value of Money
- Annuities
- Capital Budgeting
- Bond Valuation
- Stock Valuation
- Risk and Return
- CAPM
- WACC
- Capital Structure
15 questions
Try each one before you open its answer.
1. You deposit $5,000 today in an account that pays 6% annual interest (APR), compounded monthly. How much will be in the account after 10 years, rounded to the cent?
- A $8,954.24
- B $5,255.70
- C $9,096.98
- D $8,000.00
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Answer: C. $9,096.98
With monthly compounding the rate is 6% ÷ 12 = 0.5% per month for 10 × 12 = 120 months, so FV = $5,000 × 1.005^120 = $9,096.98. Compounding once a year would give $8,954.24, and using 0.5% for only 10 periods gives $5,255.70.
2. An investment of $2,000 grows to $3,500 in 7 years with annual compounding. What annual rate of return did it earn? Round to two decimal places of a percent.
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Answer: 8.32%
Solve $2,000 × (1 + r)^7 = $3,500: (1 + r)^7 = 1.75, so r = 1.75^(1/7) − 1 = 8.32%. Dividing the 75% total gain by 7 years (10.71%) ignores compounding.
3. You borrow $25,000 for a car at 6% APR with monthly payments over 5 years, the first payment due one month from today. What is the monthly payment, rounded to the cent?
- A $483.32
- B $494.58
- C $541.67
- D $416.67
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Answer: A. $483.32
The loan is the present value of a 60-payment ordinary annuity at 0.5% per month, so PMT = $25,000 × 0.005 ÷ (1 − 1.005^(−60)) = $483.32. $416.67 ignores interest, and $541.67 adds simple interest of $7,500 and divides by 60.
4. You deposit $3,000 at the beginning of each year for 30 years into an account that earns 7% compounded annually. How much will the account hold at the end of year 30, rounded to the cent?
- A $283,382.36
- B $90,000.00
- C $22,836.77
- D $303,219.12
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Answer: D. $303,219.12
Deposits at the start of each year form an annuity due, worth the ordinary-annuity future value times (1 + r): $3,000 × [(1.07^30 − 1) ÷ 0.07] × 1.07 = $303,219.12. The $283,382.36 answer treats the deposits as made at the end of each year, so each one earns one year less interest.
5. A project costs $100,000 today and is expected to produce cash flows of $30,000, $40,000, $50,000 and $20,000 at the end of years 1 through 4. At a 10% discount rate, what is its NPV, rounded to the cent?
- A $40,000.00
- B $11,556.59
- C $111,556.59
- D $27,272.73
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Answer: B. $11,556.59
Discount each cash flow to today: $30,000 ÷ 1.1 + $40,000 ÷ 1.1² + $50,000 ÷ 1.1³ + $20,000 ÷ 1.1⁴ = $27,272.73 + $33,057.85 + $37,565.74 + $13,660.27 = $111,556.59. Subtracting the $100,000 cost gives an NPV of $11,556.59, so the project earns more than 10% and should be accepted.
6. A project costs $10,000 today and returns $4,000 at the end of each of the next 3 years. What is its internal rate of return? Round to two decimal places of a percent.
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Answer: 9.70%
The IRR is the rate that makes NPV zero: $4,000 × [1 − (1 + r)^(−3)] ÷ r = $10,000, so the 3-year annuity factor must equal 2.5. Solving by trial or with a financial calculator gives r = 9.70%.
7. A project costs $50,000 and is expected to return $15,000, $20,000, $25,000 and $10,000 in years 1 through 4. Assuming the cash flows arrive evenly through each year, what is its payback period?
- A 3.00 years
- B 2.86 years
- C 3.33 years
- D 2.60 years
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Answer: D. 2.60 years
After 2 years the project has recovered $15,000 + $20,000 = $35,000, leaving $15,000 to recover from the $25,000 of year 3. That takes $15,000 ÷ $25,000 = 0.6 of a year, so payback is 2.60 years.
8. A bond has a $1,000 face value, a 6% coupon rate paid semiannually, and 10 years to maturity. If its yield to maturity is 8% (an annual rate compounded semiannually), what is its price, rounded to the cent?
- A $864.10
- B $1,000.00
- C $1,148.77
- D $456.39
Show answer
Answer: A. $864.10
Use semiannual periods: 20 coupons of $30 discounted at 4%, plus $1,000 at the end of period 20. Price = $30 × [1 − 1.04^(−20)] ÷ 0.04 + $1,000 ÷ 1.04^20 = $407.71 + $456.39 = $864.10, below face value because the coupon rate is below the yield.
9. A bond with a $1,000 face value and a 5% coupon paid annually has 4 years left to maturity and sells for $950. What is its yield to maturity? Round to two decimal places of a percent.
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Answer: 6.46%
The YTM is the rate r that solves $50 × [1 − (1 + r)^(−4)] ÷ r + $1,000 ÷ (1 + r)^4 = $950, which a financial calculator gives as 6.46%. It is above both the 5% coupon rate and the 5.26% current yield ($50 ÷ $950) because it also counts the $50 gain from buying at $950 and receiving $1,000 at maturity.
10. A company just paid a dividend of $2.00 per share. Dividends are expected to grow at 5% a year forever, and investors require a 12% return. Using the constant-growth dividend discount model, what is the stock worth today?
- A $28.57
- B $17.50
- C $30.00
- D $12.35
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Answer: C. $30.00
The model uses next year's dividend: D1 = $2.00 × 1.05 = $2.10. Price = D1 ÷ (r − g) = $2.10 ÷ (0.12 − 0.05) = $30.00; using the $2.00 just paid instead gives $28.57.
11. A stock is expected to pay dividends of $1.00 at the end of year 1 and $1.50 at the end of year 2, after which dividends will grow at 4% a year forever. If the required return is 10%, what is the stock worth today, rounded to the cent?
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Answer: $23.64
At the end of year 2 the stock is worth D3 ÷ (r − g) = ($1.50 × 1.04) ÷ (0.10 − 0.04) = $26.00. Discount the dividends and that price to today: $1.00 ÷ 1.10 + ($1.50 + $26.00) ÷ 1.10² = $0.91 + $22.73 = $23.64.
12. A stock's return next year is expected to be 25% in a boom (probability 0.3), 10% in a normal economy (probability 0.5), and −15% in a recession (probability 0.2). What is its expected return?
- A 6.67%
- B 9.50%
- C 15.50%
- D 13.87%
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Answer: B. 9.50%
Expected return is the probability-weighted average: 0.3 × 25% + 0.5 × 10% + 0.2 × (−15%) = 7.5% + 5.0% − 3.0% = 9.50%. A simple average of the three outcomes (6.67%) ignores the probabilities, and 13.87% is the standard deviation, a measure of risk rather than return.
13. The risk-free rate is 4%, the expected return on the market is 10%, and a stock's beta is 1.3. According to the CAPM, what is the stock's required return?
- A 11.80%
- B 13.00%
- C 17.00%
- D 7.80%
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Answer: A. 11.80%
Required return = risk-free rate + beta × (market return − risk-free rate) = 4% + 1.3 × (10% − 4%) = 4% + 7.8% = 11.80%. Multiplying beta by the whole 10% market return instead of the 6% market risk premium leads to the wrong answers 13.00% and 17.00%.
14. A firm's capital structure, at market values, is $60 million of equity and $40 million of debt. Its cost of equity is 12%, its pre-tax cost of debt is 6%, and its tax rate is 25%. What is its weighted average cost of capital (WACC)?
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Answer: 9.00%
The weights are 60% equity and 40% debt, and debt enters at its after-tax cost of 6% × (1 − 0.25) = 4.5% because interest is tax-deductible. WACC = 0.60 × 12% + 0.40 × 4.5% = 7.2% + 1.8% = 9.00%.
15. According to the Modigliani-Miller propositions for a world with no taxes, no bankruptcy costs and no other market frictions, what happens when a firm issues debt and uses the money to buy back some of its stock?
- A Its WACC falls because debt is cheaper than equity, so the firm becomes more valuable
- B Its cost of equity stays the same because the business risk of its assets has not changed
- C Its cost of equity and its WACC both rise, so the firm becomes less valuable
- D Its cost of equity rises, but its WACC and total firm value stay the same
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Answer: D. Its cost of equity rises, but its WACC and total firm value stay the same
With no taxes or frictions, firm value depends only on the cash flows from its assets, so splitting them differently between debt and equity does not change it (Proposition I). More debt makes the remaining equity riskier, so the cost of equity rises just enough to offset the cheaper debt and leave WACC unchanged (Proposition II).