Question

Your grandmother is a cautious person and chooses to invest in bonds only. She buys a bond that guarantees a payment of $80 at the end of each year for the next 10 years. As well, when the last dividend it paid, she also receives a principal payment of $800.

a. What is the present discounted value of the bond if the discount rate is 10%?

b. What is the present discounted value of the bond if the discount rate is 15%?

c. If your grandmother paid $800 for the bond initially, did she make a good investment? Explain how your answer depends on the discount rate.

Answer 1

ANSWER:

a) I = 10%

n = 10 years

future value = $800

annual payment received = $80

pv = fv(p/a,i,n) + annual payment received(p/a,i,n)

pv = 800(p/f,10%,10) + 80(p/a,10%,10)

pv = 800 * 0.3855 + 80 * 6.145

pv = 308.4 + 491.6

pv = 800

b) i = 15%

n =10 years

future value = $800

annual payment received = $80

pv = fv(p/a,i,n) + annual payment received(p/a,i,n)

pv = 800(p/f,15%,10) + 80(p/a,15%,10)

pv = 800 * 0.2472 + 80 * 5.019

pv = 197.76 + 401.52

pv = 599.28

c) if my grandmother paid $800 initially then if the discount rate is 10% , then she is indifferent as the amount she will receive over the years will be equal to $800 ( in present value) while if the discount rate is 15% , then the decision is wrong as the present value of the money received will be $599.25 which is less then $800 and hence only if the discount rate is below 10% , then only she will benefit.