Question

You will receive $697 at the end each year in years 1 through 10, $2,024 in years 11 through 20, and $2,547 in years 21 through 30. How much is all this worth today, if the required rate of return is 8%?

GDebi, Inc. plans to issue 5.5 percent coupon bonds, with annual coupon frequency, 14 years to maturity and $1000 face value. If the prevailing market yield on bonds of similar riskiness and maturity is 6.1 percent, what would be the market price of GDebi's bonds?

Answer 1

Answer to First Part

Year	Annual Cash Flow ($)	Present Value factor at 8%	Present Value of Cash Flow ($)
1	697	0.92593	645.37
2	697	0.85734	597.57
3	697	0.79383	553.30
4	697	0.73503	512.32
5	697	0.68058	474.37
6	697	0.63017	439.23
7	697	0.58349	406.69
8	697	0.54027	376.57
9	697	0.50025	348.67
10	697	0.46319	322.85
11	2,024	0.42888	868.06
12	2,024	0.39711	803.76
13	2,024	0.36770	744.22
14	2,024	0.34046	689.09
15	2,024	0.31524	638.05
16	2,024	0.29189	590.79
17	2,024	0.27027	547.02
18	2,024	0.25025	506.50
19	2,024	0.23171	468.99
20	2,024	0.21455	434.25
21	2,547	0.19866	505.98
22	2,547	0.18394	468.50
23	2,547	0.17032	433.79
24	2,547	0.15770	401.66
25	2,547	0.14602	371.91
26	2,547	0.13520	344.36
27	2,547	0.12519	318.85
28	2,547	0.11591	295.23
29	2,547	0.10733	273.36
30	2,547	0.09938	253.11
TOTAL			14,634.41

“The total worth today of the amount received = $14,634.41”

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.

Answer to Second Part

The Market Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the bond = $1,000

Annual Coupon Amount = $55 [$1,000 x 5.50%]

Annual Yield to Maturity = 6.10%

Maturity Period = 14 Years

The Market Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $55[PVIFA 6.10%, 14 Years] + $1,000[PVIF 6.10%, 14 Years]

= [$55 x 9.23770] + [$0.43650]

= $508.07 + $436.50

= $944.57

“Therefore, the the market price of GDebi's bond = $944.57”

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.  

--The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.