Question

Kelly Industries issued 7% bonds, dated January 1, with a face value of $100,000 on January 1, 2021. The bonds mature in 2031 (10 years). Interest is paid semiannually on June 30 and December 31. For bonds of similar risk and maturity the market yield is 8%. What was the issue price of the bonds? FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.) Multiple Choice 0 O $93,205. 0 $98,401. 0 $47,566. 0 $75,418.

Answer 1

Price of a bond is the present value of all future cash flows from it discounted at a required rate of return. This required rate of return is the YTM. YTM is the yield the bond-holder earns when the bond is held till its maturity. The cash flows from a bond are periodic coupon payments and the redemption of face value on maturity. • Interest is always paid on face value: $100,000 x 3.5% = $3,500 o Annual coupon rate = 7%. Since coupon payment is semi-annual, rate per period of 6 months = 7% = 2 = 3.5% When Cash flows are non-annual convert the years to maturity into periods. Thus, there are 20 periods (10 years x 2 periods of 6 months) . The YTM of the bond is the required rate of return or market rate of interest 'i' = 4% O Annual YTM = 8%; YTM for 6 months = 8%+2 = 4% Bond cash flows are discounted using this discount rate.

Bond interest payments are in the form of annuity. So PVAF for 4%, 20 time periods is used to discount interest cash flows. • Principal should be discounted using PV factor for 20th period, 4% P Present Value Annuity Factor PVAF = = 1-(1+i)- • • i = interest rate per period = 4% n = number of periods = 20 = 13.59033 0.04 • PVAF - 1-(1+0.04)-20 PV factor = (1 + i)n . • • i = interest rate per period = 4% n = 20 PVF = 7 (1+0,04)20 = 0.45639

Cash flow Present Value Description ($) ($) Time period 1-20 20 PV Factor or PVAF 13.59033 0.45639 Interest Principal 3,500 100,000 PRICE OF THE BOND 47,566 45,639 93,205