SWH Corporation issued bonds on January 1, 2018. The bonds had a coupon rate of 4.5%,...

SWH Corporation issued bonds on January 1, 2018. The bonds had a coupon rate of 4.5%, with interest paid semiannually. The face value of the bonds is $1,000 and the bonds mature on January 1, 2028. What is the intrinsic value (to the nearest dollar) of an SWH Corporation bond on January 1, 2022 to an investor with a required return of 6%

Solutions

Expert Solution

Intrinsic value is to be calculated on January 1, 2022 and the bond will mature on January 1, 2028

So, Time left to maturity = 2028- 2022

= 6 years

When interest is paid semi-annually, interest rate is divided by 2 and time period is multiplied by 2

So, Interest rate for discounting

= 6 / 2

= 3% per period of 6 months

Time = 6 x 2

= 12 periods each of 6 months

Semi- Annual coupons

= Face Value of bond x Coupon rate x 6 / 12 months

= $1,000 x 4.5% x 6 / 12

= $22.50

Price of a bond is the present value of all future cash flows receivable from the bond discounted at required rate of return

Future cash flows are periodic interest payments and maturity value of the bond

Present value factor

= 1 / ( 1 + Rate of discounting ) ^ Number of periods

So, discounting factor for period 2

= 1 / ( 1.03 ^ 2 )

= 1 / 1.0609

= 0.942596

The following table shows the calculations

Calculations	A	B	C = A x B
Period	Cash Flow	PV Factor	Present Value
1	22.5	0.970874	21.84
2	22.5	0.942596	21.21
3	22.5	0.915142	20.59
4	22.5	0.888487	19.99
5	22.5	0.862609	19.41
6	22.5	0.837484	18.84
7	22.5	0.813092	18.29
8	22.5	0.789409	17.76
9	22.5	0.766417	17.24
10	22.5	0.744094	16.74
11	22.5	0.722421	16.25
12	22.5	0.701380	15.78
12	1000	0.701380	701.38
		Price	925.34

So, as per above calculations, the intrinsic value as on January 1, 2022 will be $ 925.34

jeff jeffy answered 1 year ago

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