Question

You bought one of Great White Shark Repellant Co.’s 5.8 percent coupon bonds one year ago for $1,030. These bonds make annual payments and mature 14 years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 5.1 percent. What was the total return?

Answer 1

total rate of return on the Bond = 9.40%

Step-by-step explanation:

given data

coupon bonds = 5.8%

bonds price = $1,030

maturity time = 14 year

required return on the bonds = 5.1 percent

solution

we know here market price of the bond is Present Value of Coupon Payments + Present face Value

so that face Valueof bond = $1,000

and here annual Coupon Amount will be

annual coupon amount = $1000 × 5.80%

annual coupon amount = $58

and here Market Price of the Bond will be

Market Price of Bond = Present Value of Coupon Payments + Present face Value ......................1

here Present Value of Coupon Payments at PVIFA 5.10% and 14 Years

Present Value Annuity Inflow Factor (PVIFA) =
`(1-(1/(1+r)^t)/(r)` ....2

Present Value Annuity Inflow Factor =
`(1-(1/(1+0.0510)^14)/(0.0510)`

Present Value Annuity Inflow Factor = 9.83566

and

Present Value Inflow Factor (PVIF) 5.10%, 14 Years=
`(1)/((1+r)^t)` ...........3

Present Value Inflow Factor (PVIF) =
`(1)/((1+0.0510)^14)`

Present Value Inflow Factor = 0.49838

so

Market Price of Bond = ( $58 × 9.83566 ) + ( $1,000 × 0.49838 )

Market Price of Bond = $1,068.85

so total rate of return on the Bond will be

total rate of return on the Bond = [ { Annual Coupon Amount + ( Change in Bond Price ) } ÷ Current Price] ...............4

total rate of return on the Bond =
`(58+(1068.85-1030))/(1030)`

total rate of return on the Bond = 9.40%