Hello,

I found a tutor's step by step explanation of a finance question, but I do not know how to calculate the PVIF and PVAF, so I can't complete the steps the tutor mentions. how were those two terms calculated?

Question:

Bonds of Orange Computers and Peach Computers are identical in all respect, including risk class. The only difference is that they have different coupon. Orange Computer bond has a semiannual coupon of $47.50 and Peach Computers bond has a semiannual coupon of $40.00. Both bonds have 8 years to maturity. The Orange Computer bond is selling in the market for $1,151.18.

What is the yield to maturity of Orange Computers bond?

What is the price of Peach Computers bond?

Can you please advise?

Tutor's Step-by-step explanation

1) Question

Orange Computers

Face Value of Bond = $ 1,000 (Assumed)

Semi Annual Coupon Amount = $ 47.50

Current Price = $ 1,151.18

Maturity = 8 Years = 8* 2 = 16 Semi Annual Period

Price of Bond is Given By:

P0 = Coupon Amount * Present Value Annuity Factor (YTM %, n Period) + Face Value * Present Value Interest Factor (YTM %, n Period)

P0 = Coupon Amount * PVAF (YTM%, n Period) + Face Value * PVIF (YTM%, n Period)

1151.18 = 47.50 * PVAF (YTM %, 16 Semi Annual Period) + 1,000 * PVIF (YTM%, 16 Semi Annual Period)

YTM will be calculated through Hit and Trial Method:

Let YTM = 3.00%

Price of Bond at 3.00 % YTM = 47.50 * PVAF (3.00 %, 16 Semi Annual Period) + 1,000 * PVIF (3.00 %, 16 Semi Annual Period)

= 47.50 * 12.561102 + 1000 * 0.6231669

= 596.6523 + 623.1669

= $ 1,219.8192

Let YTM = 4.00 %

Price of Bond at 4.00 % YTM = 47.50 * PVAF (4.00 %, 16 Semi Annual Period) + 1,000 * PVIF (4.00 %, 16 Semi Annual Period)

= 47.50 * 11.6522956 + 1000 * 0.5339081

= 553.4840 + 533.9081

= $ 1087.3920

So YTM by Interpolation Method =

= 3.00 + ( 4.00-3.00 ) * (1219.8192 - 1151.18) / (1219.8192 - 1087.3920)

= 3.50 % , So , YTM of Bond = 3.50% per Semi Annual Period

YTM of Bond Annually Rate = 3.50 *2 = 7.00 % P.a = 7.00% P.a.

2) Question

Peach Computers

Face Value of Bond = $ 1,000 (Assumed)

Semi Annual Coupon Amount = $ 40.00

Maturity = 8 Years = 8* 2 = 16 Semi Annual Period

YTM = 7.00% P.a=7 /2 = 3.50% Per Semi Annual Period it is equal to YTM of Orange Computers, because both are identical in all Respects.

Price of Bond is given by:

P0 = Coupon Amount * Present Value Annuity Factor (YTM%, n Period) + Face Value * Present Value Interest Factor (YTM %, n Period)

= Coupon Amount * PVAF (YTM%, n Period) + Face Value * PVIF (YTM%, n Period)

= 40 * PVAF (3.50%, 16 Semi Annual Period) + 1,000 * PVIF (3.50 %, 16 Semi Annual Period)

= 40 * 12.0941168 + 1,000 * 0.5767059

= 483.7646 + 576.7059

= $ 1060.47 So Price of Bond = $1060.47 (Rounded Off)