Question

Do the following present value problems. You must set up all present value problems before calculation. Merely writing down the answer (even if it is correct) is an automatic zero. You must show your work.

a. Suppose we have a four year fixed-payment loan with $1000 payments made at the end of each year. Given a market interest rate of 12 percent, how much was initially borrowed?

b. Suppose you were considering purchasing a $5000 machine today that would generate additional net profit of $2000 booked at the end of each year. Assuming you need a 15 percent return to justify the investment, would the investment be worth doing if you had only three years of payouts? Would your answer change if you had four years of $2000 payouts? Why or why not.

c. Consider two zero coupon bonds in which you receive $100 at the maturity date, one maturing in three years and one maturing in five years. Both are currently priced to yield 6 percent. Calculate the current market value of each bond?

Answer 1

a. Suppose we have a four year fixed-payment loan with $1000 payments made at the end of each year. Given a market interest rate of 12 percent, how much was initially borrowed?

Ans: PV = amount initially borrowed

= $1000 / 1.12 + $1000/1.12^2 + $1000/1.12^3 + $1000/1.12^4

= $3037.35

b. Suppose you were considering purchasing a $5000 machine today that would generate additional net profit of $2000 booked at the end of each year. Assuming you need a 15 percent return to justify the investment, would the investment be worth doing if you had only three years of payouts? Would your answer change if you had four years of $2000 payouts? Why or why not.

Ans: NPV = PV of Net profit stream - $5000

If three years, then it is:

$2000/1.15 + $2000/1.15^2 + $2000/1.15^3 - 5000

= $4566.45 - $5000 = -$433.55

I won't go for it.

If four years, then it is

$2000/1.15 + $2000/1.15^2 + $2000/1.15^3 + $2000/1.15^4 - 5000

= $5709.66 - $5000 = $709.66

I would go for it.

c. Consider two zero coupon bonds in which you receive $100 at the maturity date, one maturing in three years and one maturing in five years. Both are currently priced to yield 6 percent. Calculate the current market value of each bond?

Ans: Current market price = PV of maturity value

For 3 year bond it is: $100/1.06^3 = $83.96

For 5 year bond it is: $100/1.06^5 = $74.73