Question

Given the following yield curve: One-year bonds yield 8.50%, two-year bonds yield 9.50%, three-year bonds and greater maturity bonds all yield 10.50%. All bonds are paying annual coupons of 9.50%, once a year. You strongly believe that at year-end the yield curve will be flatten around the 3 year rate. Calculate the one year total rate of return for the one-year bond.

Answer 1

One year rate of return will be = 8.49%

Step-by-step explanation:

Data Given:

One year bonds yield = 8.50%

Two Year Bonds Yield = 9.50%

Three Year Bonds Yield = 10.50%

Coupon = 9.50%

In this question, we are asked to calculate just one year total rate of return for the one-year bond only.

Solution:

Face value of the bond = $1000

For Current Price of One year bond, we need to use excel function.

But first multiply the coupon rate with face value i.e 0.0950 x 1000 = 95

= PV (0.0850, 1, -95, -1000)

Enter the above formula into excel to get the current price of the one year bond.

So,

= PV (0.0850, 1, 95, -1000) = $1009.22

Current Price of the bond = $1009.22

After 1 year, it will mature.

So,

Price of bond at the end of year.

So, now the excel function will be:

= PV (0.0850, 0, -95, -1000) = $1000

Price of bond at the end of year = $1000

Coupon rate = 9.50%

Coupon = 1000 x 0.0950

Coupon = 95

One year rate of return will be = (Price of the bond at the end of year + Coupon - Current price of the bond) divided by Current price of the bond.

One year rate of return will be = ($1000 + 95 - $1009.22)/$1009.22

One year rate of return will be = 0.0849 x 100

One year rate of return will be = 8.49%