Fundamentals of Corporate Finance - Chapter 4 and 5 Solutions - Business Finance PDF

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Fundamentals of Corporate Finance - Chapter 4 and 5 Solutions...

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Fundamentals of Corporate Finance Third European Edition

Solutions Manual Chapter 5 questions that are relevant to teaching week 4 only Note: This is an extract from chapter 5 questions, you will only find questions that are relevant to teaching week 4 listed here. That is, questions 1-3, 5, 6, 9. For a complete list of chapter 5 questions, see teaching week 5. BASIC 1.

Present Value and Multiple Cash Flows Investment X offers to pay you £6,000 per year for nine years, whereas Investment Y offers to pay you £8,000 per year for six years. Which of these cash flow streams has the higher present value if the discount rate is 5 per cent? If the discount rate is 15 per cent? Answer: To find the PVA, we use the equation: PVA = C({1 – [1/(1 + r)t] } / r ) At a 5 per cent interest rate: X@5%:

PVA = £6,000{[1 – (1/1.059) ] / 0.05 } = £42,646.93

Y@5%:

PVA = £8,000{[1 – (1/1.056) ] / 0.05 } = £40,605.54

And at a 15 per cent interest rate: X@15%: PVA = £6,000{[1 – (1/1.159) ] / 0.15 } = £28,629.50 Y@15%: PVA = £8,000{[1 – (1/1.156) ] / 0.15 } = £30,275.86 Notice that the PV of project X has a greater PV at a 5 per cent interest rate, but a lower PV at a 15 per cent interest rate. The reason is that X has greater total cash flows. At a lower interest rate, the total cash flow is more important since the cost of waiting (the interest rate) is not as great. At a higher interest rate, Y is more valuable since it has larger annual cash flows. At the higher interest rate, these bigger annual cash flows coming early are more important since the cost of waiting (the interest rate) is so much greater.

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Fundamentals of Corporate Finance Third European Edition

2.

Future Value and Multiple Cash Flows Herlige Narren AS has identified an investment project with the following cash flows. If the discount rate is 10 per cent, what is the future value of these cash flows at the end of year 5? What is the future value at a discount rate of 15 per cent? At 20 per cent? Assume all the cash flows have occurred at the beginning of the year. Year

Cash flow (DKK)

1

950

2

1,190

3

1,540

4 1,905 Answer: To solve this problem, we must find the FV of each cash flow and add them. To find the FV of a lump sum, we use: FV = PV(1 + r)t FV@10% = DKK950(1.10)4 + DKK1,190(1.10)3 + DKK1,540(1.10)2 + DKK1,905(1.10) = DKK6,933.69 FV@15% = DKK950(1.15)4 + DKK1,190(1.15)3 + DKK1,540(1.15)2 + DKK1,905(1.15) = DKK7,698.80 FV@20% = DKK950(1.10)4 + DKK1,190(1.10)3 + DKK1,540(1.10)2 + DKK1,905(1.10) = DKK8,529.84

3.

Calculating Annuity Present Value An investment offers €4,000 per year for 10 years, with the first payment occurring one year from now. If the required return is 9 per cent, what is the value of the investment? What would the value be if the payments occurred for 20 years? For 50 years? For ever? Answer: To find the PVA, we use the equation:

PV = C x ATr

The value if the payments occurred for 10 years PV = C x A100.09 = €4000 x 6.42 PV = €25,670.63

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Fundamentals of Corporate Finance Third European Edition

The value if the payments occurred for 20 years PV = C x A200.09 = €4000 x 9.1285 PV = €36,514.18 The value if the payments occurred for 50 years PV = C x A500.09 = €4000 x 10.9617 PV = €43,846.73 The value if the payments occurred for forever

€4000 PV = 0.09 PV = €44,444.44

5.

Calculating Annuity Values You want to have DKr450,000 in your savings account 10 years from now, and you’re prepared to make equal annual deposits into the account at the end of each year. If the account pays 7 per cent interest, what amount must you deposit each year?

Answer: Here we have the FVA, the length of the annuity, and the interest rate. We want to calculate the annuity payment. Using the FVA equation: FVA = C{[(1 + r)t – 1] / r} Dkr450,000 = C[(1.0710 – 1) / .07] We can now solve this equation for the annuity payment. Doing so, we get: C = Dkr450,000 / 13.816448 = Dkr32,569.88 Calculating Perpetuity Values An investor purchasing a British consol is entitled to receive annual payments from the British government forever. What is the price of a consol that pays £4 annually if the next payment occurs one year from today? The market interest rate is 4 per cent. Answer: This cash flow is a perpetuity. To find the PV of a perpetuity, we use the equation: 6.

PV = C / r PV = £4 / 0.04 = €100

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Fundamentals of Corporate Finance Third European Edition

9.

Calculating Future Values If you invest €1,000 in a savings account that pays 4 per cent every year, how long would it take to triple your money?

Answer: PV = €1,000; r = 4%; FV = 3 x PV = €3,000; t = ? PV = FV /(1 + r)t 1,000 = 3,000/(1.04)t Solve for t. 1.04t =3 tIn(1.04) = In 3 t = In3/ In(1.04) = 28.01 years

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