A newly issued bond pays its coupons once annually. Its coupon rate is 5%, its maturity is 20 years, and its yield to maturity is 8%. a. Find the holding-period return for a 1-year investment period if the bond is selling at a yield to maturity of 7% by the end of the year.

Holding Period return 19.54%

Explanation:

We purchase to get a yield of 8%

so we sovle for the present value of the bond (market value) which is the amount at which we adquire the bond:

PV of the coupon payment:

C($1,000 x 5%) 50.000

time 20 years

rate0.08

PV$490.9074

Pv of maturity:

Maturity   1,000.00

time   20.00

rate  0.08

PV   214.55

PV c$490.9074

PV m  $214.5482

Total$705.4556

Then, we solve for the price that 7% YTM after a year:

C50.000

time19

rate0.07

PV$516.7798

Maturity   1,000.00

time   19.00

rate  0.07

PV   276.51

PV c$516.7798

PV m  $276.5083

Total$793.2881

Now we compare to get hte capital gain:

year-end less beginning value

$793.29 - $705.46  =  $87.83

The coupon is also a return:

$1,000 x 5% = $50

Total return $137.83

Investment $705.46

Holding-period return

137.83/705.46 = 0,195376 = 19.54%

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