LOS d, (Part 3): Calculate and interpret a perpetuity (PV only).

1、Compute the present value of a perpetuity with $100 payments beginning four years from now. Assume the appropriate interest rate is 10 percent/yr.

A)   $683.

B)   $751.

C)   $909.

D)   $1000.

A)   $500.

B)   $100 million.

C)   $10,000.

D)   $1,000.

A)   $1,093.

B)   $875.

C)   $700.

D)   $70.

A)   $44.12.

B)   $31.88.

C)   $37.50.

D)   $42.10.

答案和详解如下：

LOS d, (Part 3): Calculate and interpret a perpetuity (PV only).

1、Compute the present value of a perpetuity with $100 payments beginning four years from now. Assume the appropriate interest rate is 10 percent/yr.

A)   $683.

B)   $751.

C)   $909.

D)   $1000.

The correct answer was B)

Compute the present value of the perpetuity at (t=3). Recall, the present value of a perpetuity or annuity is valued one period before the first payment. So, the present value at t=3 is 100/0.10 = 1,000. Now it is necessary to discount this lump sum to t=0. Therefore, present value at t=0 is 1,000/(1.10)³ = 751

2、An investment offers $100 per year forever. If Peter Wallace’s required rate of return on this investment is 10 percent, how much is this investment worth to him?

A)   $500.

B)   $100 million.

C)   $10,000.

D)   $1,000.

The correct answer was D)     

For a perpetuity, PV = PMT/I= 100/0.10 = 1,000

3、Given investors require an annual return of 12.5 percent, a perpetual bond (i.e., a bond with no maturity/due date) that pays $87.50 a year in interest should be valued at:

A)   $1,093.

B)   $875.

C)   $700.

D)   $70.

The correct answer was C)

87.50/.125=$700.

4、Nortel Industries has a preferred stock outstanding that pays (fixed) annual dividends of $3.75 a share. If an investor wants to earn a rate of return of 8.5 percent, how much should he be willing to pay for a share of Nortel preferred stock?

A)   $44.12.

B)   $31.88.

C)   $37.50.

D)   $42.10.

The correct answer was A)

PV = 3.75/0.085 = $44.12.