Question

• in front of you 3 investments oppotunities in bonds as follow :

Bond	A	B	C
Par value	2000	5000	8000
Coupon rate	9%	11%	6%
Years to maturity	8	12	15
Market rate	15%	8%	6%
Market price	1350	6500	8100

Answer the next questions showing the steps of solving          (writing only the answers not acceptable):

1. Find the intrinsic value for the three bonds?
2. Which bond is best investment from your own opinion and why?
3. After 5 years from now assuming that the market rate remain as is, and the market price remain as is too, recalculate the intrinsic value for the three bonds?

Answer 1

1)

	A	B	C
PAR VALUE	2000	5000	8000
COUPON RATE	9%	11%	6%
COUPON AMOUNT	=2000*9% = 180	=5000*11% = 550	=8000*6% = 480
YEARS TO MATURITY	8	12	15
MARKET RATE	15%	8%	6%

Calculation of Intrinsic Value of Bond :

Value of Bonds = Present Value of Coupons + PV of Principal Amount
                       
Bond A :
                        = [PVAF (15%,8) * 180] + [PVIF (15%,8) * 2000]
= (4.4873 * 180) + (0.3269 * 2000)
                        = $807.72 + $653.80
= $1461.52

Bond B :
                        = [PVAF (8%,12) * 550] + [PVIF (8%,12) * 5000]
= (7.5361 * 550) + (0.3971 * 5000)
                        = $4144.84 + $1985.50
= $6130.34

Bond C :
                        = [PVAF (6%,15) * 480] + [PVIF (6%,15) * 8000]
= (9.7122 * 480) + (0.4173 * 8000)
                        = $4661.88 + $3338.40
= $8000 (rounded of)

Present Value Factor have been calculated as = (1/1+r)n

Where
r= Required rate of Return (Market rate)
n= No of Periods

PVAF (x%,n) is calculated by adding the PV Factor of x% for n years

2)

	A	B	C
INTRINSIC VALUE	$1461.52	$6130.34	$8000
MARKET PRICE	$1350	$6500	$8100

Since Market Price of Bond A is lower than its intrinsic value, it is relatively undervalued and should be purchased.
Since Market Price of Bond B and C are higher than their intrinsic value, they are relatively overvalued and should not be purchased.

Bond A is the best investment because Market Value < Intrinsic Value.

3) Calculation of intrinsic value after 5 years :

	A	B	C
PAR VALUE	2000	5000	8000
COUPON RATE	9%	11%	6%
COUPON AMOUNT	=2000*9% = 180	=5000*11% = 550	=8000*6% = 480
YEARS TO MATURITY	8 - 5 = 3	12 – 5 = 7	15 – 5 = 10
MARKET RATE	15%	8%	6%

Calculation of Intrinsic Value of Bond :

Value of Bonds = Present Value of Coupons + PV of Principal Amount
                       
Bond A :
                        = [PVAF (15%,3) * 180] + [PVIF (15%,3) * 2000]
                         = (2.2832 * 180) + (0.6575 * 2000)
                        = $410.98 + $1315
                         = $1725.98

Bond B :
                        = [PVAF (8%,7) * 550] + [PVIF (8%,7) * 5000]
                         = (5.2064 * 550) + (0.5835 * 5000)
                        = $2863.50 + $2917.50
                         = $5781

Bond C :
                        = [PVAF (6%,10) * 480] + [PVIF (6%,10) * 8000]
                         = (7.3601 * 480) + (0.5584 * 8000)
                        = $3532.84 + $4467.20
                         = $8000 (rounded of)

	A	B	C
INTRINSIC VALUE	$1725.98	$5781	$8000