Question

Suppose that interest rates are 10%. Dan can purchase either a short term bond or a...

Suppose that interest rates are 10%. Dan can purchase either a short term bond or a consol $10. The bond pays $3 each year for three years and then pays its face value of $5 in year 4. The consol pays $1 each year forever.

What is the present value of the bond? What is the present value of the consol? Should bob purchase the bond, the consol or neither asset for $10?

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Answer #1

In case of console

Periodic coupon=R=$1 (annual)

Console cost=Co=$10

Present worth of future cash flows=PW=R/i=1/10%=$10

Net present worth=-Co+PW=-10+10=0

In case of bond

Cash flow in year 1=CF!=$3

Cash flow in year 2=CF2=$3

Cash flow in year 3=CF3=$3

Cash flow in year 4=CF4=$5

Rate of interest=10%

PW of future payments=PW=CF1/(1+i%)^1+CF2/(1+i)^2+CF3/(1+i)^3+CF4/(1+i)^4

PW of future payments=PW=3/(1+10%)^1+3/(1+10%)^2+3/(1+10%)^3+5/(1+10%)^4=$10.88

Net present worth=-Co+PW=-10+10.88=$0.88

NPV is higher in case of coupon paying bond. It should be purchased.

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