Font Paragraph Styles Bonds practice problems A bond has a c

Font Paragraph Styles Bonds- practice problems A bond has a coupon rate of 7% and has 5 years until maturity. If the current yield to maturity is 596, what is the price of the bond? what is the amount of the annual interest payment paid to the bondholder? 1. $1,086.59 An investor buys a 10-year, 7% coupon bond for $990, holds it for 1 year, and then sells the bond for $980. What was the investor\'s rate of return? a 6,06% b. What is the price of a zero coupon bond with a 20 year maturity and a yield to maturity of 6% and a par value of$100,000? $31,180 47 What is the current yield of a 10-year bond which cost $980 and has a coupon rate of 9% c. 918% d. If you paid $980 for a 10 ycar bond that pays $70 a year in interest. What is the bond\'s yield to maturity? Annual interest prnt. + ((Par-Price)/(#yrs.tomaturity)L VIN = Yield) .60 (Price) + 40(Par)

Solution

Question 1

Bond Valuation: The value of bond is the present value of the expected cashflows from the bond,discounted at Yield to Maturity(YTM).

Current Market Price of Bonds = $1087.03 (303.03+784)

Note: When face value of bond is not given, then it is general practice to take $1,000 as face value

*PVAF = (1-(1+r)^-n)/r and **PVF = 1 / (1+r)ⁿ

Question a

Investor\'s total return comprises of 2 elements-capital gain/loss (change in market price) and coupon payment.

Rate of Return = (Sale value - cost of acquisituion + coupon pay)*100 / cost of acquisituion

= (980-990+70) *100/ 990

= (60*100) / 990

= 6.06%

Question b

Price of a zero-coupon bond is the present value of future cashflows discounted at YTM. As far as a zero-coupon bond is concerned, it does not pay any coupon payments, it pays only a lump sum amount on its maturity.

Value of zero-coupon bond = Face vale / (1+YTM)^{time to maturity}

= 100,000 / 1.06²⁰

= 100,000 / 3.2071

= $31,180.82

Question c

Current Yield = Interest per annum / Current market price

= (1000*9%) / 980

= 90 / 980

= .0918

= 9.18%

Question d

Yield To Maturity(YTM) = (interest per annum + average other cost per annum) / average fund employed

Average other cost per annum = (Redemption price - Current market price) / life remaining to maturity

= (1000 - 980) / 10

= 2

Average fund employed =(.4*Redemption price) +( .6*Current market price)

= (.4*1000 )+ (.6*980)

= 400 + 588

= 988

Yield To Maturity(YTM) = (interest per annum + average other cost per annum) / average fund employed

= (70+2) / 988

= 72 / 988

= 7.29%

Year	Cash flow	PVAF/PVF@5%	Present Value (Cashflow*PVAF/PVF)
1-5	70	4.329*	303.03
5	1000	0.784**	784.00