The YTM on a bond is the interest rate you earn on your investment if interest r

Question

The YTM on a bond is the interest rate you earn on your investment if interest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY). Requirement 1: Suppose that today you buy an annual coupon bond with a coupon rate of 8.1 percent for $905. The bond has 8 years to maturity. What rate of return do you expect to earn on your investment? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Rate of return % Requirement 2: Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. (a) What price will your bond sell for? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Price $ (b) What is the HPY on your investment? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Holding period yield %

Explanation / Answer

Requirement 1:

Calculation OF Required Rate of Return:

Given data,

Market Price = $905

Coupon Rate = 8.1%

Years to Maturity = 8

Let Par Value = Maturity Value = $1000

Interest = $1000 * 8.1% = $81

Let Yield to Maturity be x

Market Price = [PV of Interest] + [PV of Maturity Value]

$905 = [81 * PVAF(x%, 8)] + [1000 * PVIF(x%, 8)]

At x=9%,

Market Price = (81*5.5348) + (1000*0.5019)

= 448.3188 + 501.9

= 950.2188

At x=10%,

Market Price = (81*5.3349) + (1000*0.4665)

=432.1269 + 466.5

= 898.6269

For 1% increase in YTM, there is a decrease of $51.5919 (950.2188-898.6269) in Value of Bond.

For how much increase in YTM, there is a decrease of $45.2188 (950.2188-905) in Value of Bond.

Answer is 0.87647% (45.2188/51.5919)

Therefore, YTM = 9 + 0.87647 = 9.87647%

Required Rate of Return = Yield to Maturity = 9.88%

Requirement 2:

Yield to Maturity declined by 1%.

Yield to Maturity = 9.88 – 1 = 8.88%

a)Calculation of Price of the Bond:

Price of the Bond = [81 * PVAF(8.88%, 6)] + [1000 * PVIF(8.88%, 6)]

= (81*4.5020) + (1000*0.6002)

= 364.662 + 600.2

= 964.862

Bond can be sold for $964.862

b) Calculation of Holding Period Yield:

Holding Period Yield = (Maturity Value – Purchase Value) / Purchase Value

= (964.862 - 905) / 905

= 59.862 / 905

= 0.06614

= 6.614%

Holding Period Yield = 6.61%

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