Question

Example 1

Last year, The CYS sold $40,000,000 worth of 7.5% coupon, 15-year maturity, $1000 par value, AA-rated; non-callable bonds to finance its business expansion. These bonds pay semi-annual coupon payments. At issuance, the yield to maturity was 8.4%. Currently, investors are demanding a yield of 8.5% on similar bonds.

(a)If you own one of these bonds and want to sell it, how much money can you expect to receive on it?

(b)If you can reinvest the coupons you receive at a rate of 6% (monthly compounded APR), what is your actual return from holding the bond for one year since last year?

Example 2

CYS Inc. wants to raise $3 million by issuing 10-year zero coupon bonds with a face value of $1,000. Their investment banker informs them that investors would use a 9.25% (semi-annually compounded APR) discount rate on such bonds. At what price would these bonds sell in the market place assuming semi-annual compounding? How many bonds would the company have to issue in order to raise $3 million?

Answer 1

Example 1:

(a): Sale price of the bond one year after issue=$919.03 Calculated using PV function of Excel as follows:

1 D13 fc =PV(D12,09,D10,D2)*-1 A B C Function Formula arguments Values 2 Face Value (FV) Given $1,000 3 Coupon rate (R) Given 7.50% 4 Interest frequency Given Semi annual 5 Number of coupon payments a year (n) 6 Original term (T) Given 7 Priod expired (years) (t) Given 8 Time to maturity (no. of years) (N) T-t 9 Number of future coupon payments Nin Nper 28 10 Amount of coupon payment FV*R/n PMT $37.50 11 Interest rate (YTM) Given 8.50% 12 Interest rate per period YTM/N Rate 4.25% 13 Price (Present value) PV $ 919.03

(b): YTM at the time of issue was 8.4%. At this rate, price was $924.04 as follows:

D D13 =PV(D12,09,010,D2)*-1 B Function 1 Formula arguments Values 2 Face Value (FV) Given $1,000 3 Coupon rate (R) Given 7.50% 4 Interest frequency Given Semi annual 5 Number of coupon payments a year (n) 6 Original term (T) Given 7 Priod expired (years) (t) Given 8 Time to maturity (no. of years) (N) T-t 9 Number of future coupon payments Nin Nper 30 10 Amount of coupon payment FV*R/n PMT $37.50 11 Interest rate (YTM) Given 8.40% 12 Interest rate per period YTM/N Rate 4.20% 13 Price (Present value) PV $ 924.04

First coupon of $37.50 was received after 6 months of issue. This was reinvested at 6% monthly compounded.

(i) Value of first coupon at the end of first year= $37.50*(1+6%/12)6 = $37.50* 1.030378= $38.64

(ii) Second semi annual coupon (received at the end of first year)= $37.50

Total interest income during the one year holding period (I)= $38.64+ $37.50 = $76.14

Sale price (as in part (a) above (P1)= $919.03

Actual return from holding the bond for one year= (P1-P0+I)/P0

= ($919.03-$924.04+$76.14)/ $924.04 =71.13/924.04 = 7.697719%

Example 2:

Market price of one zero coupon bond= $ 636.27563051 Rounded to $636.28

Number of bonds to be issued to raise $ 3 Million= 4714.937766 Rounded to 4,715

Details as follows:

C17 5 Values $ 1,000 Semi annual f =3000000/C14 B 4 and n=term to maturity number of years Formula 6 Face Value (F) Given 7 Compounding frequency Given 8 Times compounded a year (t) 9 Term to maturity in years (n) Given 10 YTM Yearly discount rate (R) Given 11 Discount rate per half year (r) =R/t 12 1+r 13 (1+r)^n 14 Price of one Zero coupon bond (P) F/(1+r)^n 15 16 Amount to be raised (A) 17 Number of bonds to be issued A/P 10 9.25% 4.625% 1.04625 1.57164592 636.27563051 $3 Million 4714.9377661 10