Question

a) A one-year discount bond has a face value of $1000 and price of $880. What is the yield to maturity on the bond? Report using percentages with two decimal places.

b) Suppose you have two clients who need your services for two years. One agreed to pay you $50,000 one year from now and another $50,000 in two years while the other paid $35,000 after one year, but $65,000 after two years. Assuming an interest rate of 10%, which one has a higher present value? Round off to the nearest dollar.

Answer 1

a) Future value = 1000

Present value = 880

t=1 yr

i=?

Formula for future value from present value is

F=P*(1+R)^t

now putting values into the formula

1000 = 880 * (1+i)^1

1+i = 1000/880

i= 1.13636-1

i =0.13636 = 13.636% ~ 13.64%

B) i = 10% = 0.1

t = 2 yrs

first option

50000 after 1 yr and 50000 at the end of yr 2

PV of first option = 50000/(1+0.1)^1 + 50000/(1+0.1)^2

= 45454.545 + 41322.314

= 86776.859 ~ 86777

Second option

35000 after 1 yr and 65000 at the end of yr 2

PV of second option = 35000/(1+0.1)^1 + 65000/(1+0.1)^2

= 31818.181 + 53719.008

=85537.189 ~ 85537

Option 1 has the higher net present value (86777>85537)