Question

Allied Materials needs $8 Million in new capital for the expansion of its composites manufacturing facilities. It is offering a $10,000, 5% bond at a discount price of $8000. The bond matures in 20 years and pays a Semiannual dividend.

a) What is the effective annual rate of return to an investor who buys the bond?

b) What is the effective annual rate of return to an investor who buys the bond and then resales it to the second investor in six years (just after the 12th payment) for $8750?

c) What is the effective annual rate of return to the second investor?

Use financial excel functions =RATE & =EFFECT to help solve these questions.

Answer 1

a) What is the effective annual rate of return to an investor who buys the bond?

We have following formula for calculation of bond’s yield to maturity (YTM)

Bond price P0 = C* [1- 1/ (1+YTM) ^n] /YTM + M / (1+YTM) ^n

Where,

P0 = the current market price of bond = $8,000

M = value at maturity, or par value = $ 10,000

C = coupon payment = 5% of $10,000 = $500 but semiannual coupon, therefore C = $500/2 = $250

n = Semi-annual periods to maturity = 20 *2 = 40

YTM = interest rate, or yield to maturity =?

Now we have,

$8,000 = $250 * [1 – 1 / (1+YTM) ^40] /YTM + 10,000 / (1+YTM) ^40

From above equation, we can calculate the value of YTM, which is 3.43% semiannual

Therefore annual yield to maturity of bond, YTM = 2 *3.43% = 6.85% per year

Effective annual rate = (1+3.43%) ^2 -1 = 6.97%

b) What is the effective annual rate of return to an investor who buys the bond and then resales it to the second investor in six years (just after the 12th payment) for $8750?

We have following formula for calculation of bond’s yield to maturity (YTM)

Bond price P0 = C* [1- 1/ (1+YTM) ^n] /YTM + M / (1+YTM) ^n

Where,

P0 = the current market price of bond = $8,000

M = value at maturity, or par value = $ 8,750

C = coupon payment = 5% of $10,000 = $500 but semiannual coupon, therefore C = $500/2 = $250

n = Semi-annual periods to maturity = 6 *2 = 12

YTM = interest rate, or yield to maturity =?

Now we have,

$8,000 = $250 * [1 – 1 / (1+YTM) ^12] /YTM + 8,750 / (1+YTM) ^12

From above equation, we can calculate the value of YTM, which is 3.76% semiannual

Therefore annual yield to maturity of bond, YTM = 2 *3.76% = 7.52% per year

Effective annual rate = (1+3.76%) ^2 -1 = 7.66%

c) What is the effective annual rate of return to the second investor?

We have following formula for calculation of bond’s yield to maturity (YTM)

Bond price P0 = C* [1- 1/ (1+YTM) ^n] /YTM + M / (1+YTM) ^n

Where,

P0 = the current market price of bond = $8,750

M = value at maturity, or par value = $ 10,000

C = coupon payment = 5% of $10,000 = $500 but semiannual coupon, therefore C = $500/2 = $250

n = Semi-annual periods to maturity = 14 *2 = 28

YTM = interest rate, or yield to maturity =?

Now we have,

$8,750 = $250 * [1 – 1 / (1+YTM) ^28] /YTM + 10,000 / (1+YTM) ^28

From above equation, we can calculate the value of YTM, which is 3.18% semiannual

Therefore annual yield to maturity of bond, YTM = 2 *3.18% = 6.36% per year

Effective annual rate = (1+3.18%) ^2 -1 = 6.46%

Calculation in excel:

a.			b.			c.
PV	8000		PV	8000		PV	8750
FV	10000		FV	8750		FV	10000
PMT	250		PMT	250		PMT	250
NPER	40		NPER	12		NPER	28
Rate (semiannual)	3.43%		Rate (semiannual)	3.76%		Rate (semiannual)	3.18%
Rate (annual)	6.85%		Rate (annual)	7.52%		Rate (annual)	6.36%
Rate (Effective)	6.97%		Rate (Effective)	7.66%		Rate (Effective)	6.46%