No excel A. You are considering the purchase of a coupon bond with a face value

Question

No excel

A. You are considering the purchase of a coupon bond with a face value of $1,000, which matures in 23 years, and pays 4.85% (annual) coupons. If the current market price of the bond is $979.77, estimate this Yield-to-Maturity (YTM) of the instrument. What is the YTM if the coupons are paid semi-annual?

B. One year ago you purchased a share of stock for $32.79. Today it is selling for $31.18. What is the Holding Period Return on this investment for the year? What would be the Holding Period Return if the firm had paid a dividend of $2.45 per share during the year?

Explanation / Answer

Answer to Question A:

If coupons are paid annually:

Face Value = $1,000
Current Price = $979.77

Annual Coupon Rate = 4.85%
Annual Coupon = 4.85% * $1,000
Annual Coupon = $48.50

Time to Maturity = 23 years

Let annual YTM be i%

$979.77 = $48.50 * PVIFA(i%, 23) + $1,000 * PVIF(i%, 23)

Using financial calculator:
N = 23
PV = -979.77
PMT = 48.50
FV = 1000

I = 5.0%

Yield to Maturity = 5.0%

If coupons are paid semi-annually:

Face Value = $1,000
Current Price = $979.77

Annual Coupon Rate = 4.85%
Semiannual Coupon Rate = 2.425%
Semiannual Coupon = 2.425% * $1,000
Semiannual Coupon = $24.25

Time to Maturity = 23 years
Semiannual Period to Maturity = 46

Let semiannual YTM be i%

$979.77 = $24.25 * PVIFA(i%, 46) + $1,000 * PVIF(i%, 46)

Using financial calculator:
N = 46
PV = -979.77
PMT = 24.25
FV = 1000

I = 2.499%

Semiannual YTM = 2.499%
Annual YTM = 2 * 2.499%
Annual YTM = 5.0%

Answer to Question B:

If no dividend is paid during the year:

Holding Period Yield = (Selling Price + Dividend - Purchase Price) / Purchase Price
Holding Period Yield = ($31.18 + $0 - $32.79) / $32.79
Holding Period Yield = -4.91%

If dividend of $2.45 is paid during the year:

Holding Period Yield = (Selling Price + Dividend - Purchase Price) / Purchase Price
Holding Period Yield = ($31.18 + $2.45 - $32.79) / $32.79
Holding Period Yield = 2.56%

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