Question

How do you find the Price Next Year, the Rate of Capital Gain, and the Rate of Return on a 1 year return of a bond with a 30 year maturity that has a 10% coupon rate and a face value of $1,000 and I increases from 10% to 20% in 1 year.

Answer 1

1)

Coupon = 0.1 * 1000 = $100

Current price will be same as face value as I is same as coupon rate.

Current price = $1,000

When I increases from 10% to 20%.

Price next year = Coupon *[1 - 1 / ( 1 + r)ⁿ] / r + FV / (1 + r)ⁿ

Price next year = 100 *[1 - 1 / ( 1 + 0.2)²⁹] / 0.2 + 1,000 / (1 + 0.2)²⁹

Price next year = 100 * 4.974724 + 5.055264

Price next year = $502.53

Keys to use in a financial calculator: FV 1000, PMT 100, N 29, I/Y 20, CPT PV

2)

Capital gains rate = [(ending value - beginning value) * 100]

Capital gains rate = [(502.53 - 1,000) / 1,000 )*100]

Capital gains rate = -49.75%

3)

Rate of return = [(ending value + interest- beginning value) * 100]

Rate of return = [(502.53 + 100 - 1,000) / 1,000 )*100]

Rate of return = -39.75%