York University

Department of Economics

Economics 4400: Corporate Finance I

Fall 2004 Midterm Examination with Answers

Problem 1. (3 pts) Consider an individual who lives for two two periods,

1 and 2. His income in period 1 is $100, his period 2 income is $110. The interest

rate at which he can borrow or lend is 10%.

a. What is the maximum amount that he can spend in period 2 if he

does not want to spend anything in period 1?

In period 2 he can spend his period 2 income plus the future value of the

period 1 income:

$110 + $100(1 + 10%) = $220

b. What is the maximum amount that he can spend in period 1 if he

does not want to spend anything in period 2?

He can spend the entire period 1 income plus the present value of period two

income:

$100 + $110 1

(1 + 10%) = $200:

Problem 2. (3 pts) Two stocks, A and B, had the same price two years

ago. During the last two years, A’s stock price had …rst increased by 30% and

then dropped by 30%, while B’s had …rst dropped by 30% and then increased

by 30%. Do these two stocks have the same price today? Explain.

Denote the common price of Aand Btwo years ago as p. For A, the price

…rst went up by 30% in last year was p(1 + 3

10 ):Then it dropped by 30% so the

price this year is last year’s price times (1 30%). So it is p(1 + 3

10 )(1 3

10 ) =

0:91p. Analogically, the price of Blast year was p(1 3

10 )and this year it is

p(1 3

10 )(1 + 3

10 ) = 0:91p. The prices are the same now.

Problem 3. (2 pts) Consider a world with three periods: 0, 1, and 2.

The discount rate is 0% (zero). Provide an example of two investment projects,

A, and B, such that the net present value of A is greater than the NPV of B, yet

B has the higher internal rate of return of the two. (Note: You have to present

two sequences of numbers (cash‡ow streams) a0; a1; a2and b0; b1; b2and show

that these satisfy certain inequalities).

A standard example is when one project (B) has higher percentage return

but the other (A) has greater scale. For example, consider:

1

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A:fa0=$1000; a1= $1100; a2= 0g.

B:fb0=$10; b1= $50; b2= 0g

A’s net present value is greater:

a0+a1+a2= $100 >$50 = b0+b1+b2

but Bhas higher internal rate of return:

IRRA=a1

ja0j1 = 10% <490% = b1

jb0j1 = IRRB

Problem 4. (2 pts) In the same setting as above (three periods, zero

discount rate) provide an example of two investment projects A, B such that A

has the larger NPV, yet B has the smaller (shorter) payback period.

Example:

A:fa0=$10; a1= $5; a2= $100g.A’s NPV is $105, the payback period

is 2.

B:fb0=$10; b1= $10; b2= $10g.B’s NPV is $10, the payback period is

1.

The key here is that Ahas to relatively backloaded, compared with B.

Problem 5. The probability that the economy will experience growth

next year is a, the probability of a recession is 1a. In recession, the return

on your portfolio is b%. With growth, your return will be c%. What is the

expected return and standard deviation of the portfolio? Write down formulas

in terms of a; b; c:

Expected return:

ac% + (1 a)b%

Standard deviation:

pa[c%ac% + (1 a)b%]2+ (1 a)[b%ac% + (1 a)b%]2

Problem 6. A security pays a stream of dividends which are known in

advance. The dividend is $11 in period one, $12.1 in period two. The discount

rate is 10%. If the NPV of the security is $75 in period zero, what will be the

2

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NPV of the security in period two (after the period 2 dividend is paid out)?

Explain your answer.

Price of the security in period 2 is the value of future dividends at that point:

P V2=c3

(1:1) +c4

(1:1)2+c5

(1:1)3+:::

What you are given in text is the present value of dividends as of period

zero:

$75 = P V0=c1

(1:1) +c2

(1:1)2+c3

(1:1)3:::

and period one and two dividends:

c1= $11 ; c2= $12:1

Substituting, we obtain the present (period zero) value of cash‡ows starting

from period 3:

P V0c1

(1:1) c2

(1:1)2= $55 = c3

(1:1)3+c4

(1:1)4+c5

(1:1)5+:::

We only need to convert the present calue of this cash‡ows into period two

dollars:

P V2= $55(1:1)2=c3

(1:1) +c4

(1:1)2+c5

(1:1)3+:::

Problem 7. Consider a person who will live for either 4 (with probability

50%) or 7 years (probability 50%). You are a pension plan company and consider

selling this person a security that pays c each year, as long as they are alive.

Discount rate is r. What is the maximum c that you would be willing to o¤er

that person if he/she spent $100 on this security? Assume you are risk-neutral.

Present value of paying out cfor four years is:

c

r(1 1

(1 + r)4)

Present valye of paying cout for seven years is:

c

r(1 1

(1 + r)7)

3

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