Question

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.

Answer 1

Holding Period return 19.54%

Step-by-step 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-(1+r)^(-time) )/(rate) = PV\\`

C ($1,000 x 5%) 50.000

time 20 years

rate 0.08

`50 * (1-(1+0.08)^(-20) )/(0.08) = PV\\`

PV $490.9074

Pv of maturity:

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 1,000.00

time 20.00

rate 0.08

`(1000)/((1 + 0.08)^(20) ) = PV`

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:

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 50.000

time 19

rate 0.07

`50 * (1-(1+0.07)^(-19) )/(0.07) = PV\\`

PV $516.7798

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 1,000.00

time 19.00

rate 0.07

`(1000)/((1 + 0.07)^(19) ) = PV`

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%