Question

​A(n) 8.0%, ​25-year bond has a par value of​ $1,000 and a call price of $1,075.

​(The bond's first call date is in 5​ years.) Coupon payments are made semiannually​ (so use semiannual compounding where​ appropriate).

a. Find the current​ yield, YTM, and YTC on this​ issue, given that it is currently being priced in the market at $1,200.

Which of these 3 yields is the​ highest? Which is the​ lowest? Which yield would you use to value this​ bond? Explain.

b. Repeat the 3 calculations​ above, given that the bond is being priced at ​$850.

Now which yield is the​ highest? Which is the​ lowest? Which yield would you use to value this​ bond? Explain.

Answer 1

Solution :-

(a)

(i)

Price of Bond = $1,200

Annual Coupon = $1,000 * 8.0% = $80

Current Yield = $80 / $1,200 = 6.67%

(ii)

Time to Call = 5 Years

As Semiannual (n) = 5 * 2 = 10

Semiannual Coupon = $80 / 2 = $40

Fax ERATE(C3,C4,C5,C6) B с 1 C8 A (11 2 3 Time to Call 4 Coupon payment 5 Price 6 Price to Call 7 8 Yield to Call 9 10 11 Nper Pmt PV FV 10 $40 ($1,200.00) $1,075 Rate 2.40% Formula RATE/C3,C4,C5,C6)

Now Annual Yield to Call = 2.40% * 2 = 4.80%

(iii)

Time to Maturity = 25 Years

As Semiannual (n) = 25 * 2 = 50

12 (1) 50 Nper Pmt PV $40 ($1,200.00) $1,000 FV 13 14 Time to Maturity 15 Coupon payment 16 Price 17 Face Value 18 19 Yield to Maturity 20 21 22 23 Rate 3.19% Formula RATE(C14,C15,C16,C17)

Now Annual Yield to Maturity = 3.19% * 2 = 6.38%

Now Highest Yield is Current Yield

Lowest Yield is Yield to Call

To Value the Bond we use Yield to Maturity

(b)

(i)

Price of Bond = $850

Annual Coupon = $1,000 * 8.0% = $80

Current Yield = $80 / $850 = 9.41%

(ii)

Time to Call = 5 Years

As Semiannual (n) = 5 * 2 = 10

Semiannual Coupon = $80 / 2 = $40

fx =RATE(C3,C4,C5,C6) B с C8 A 1 ) 2 3 Time to Call 4 Coupon payment 5 Price 6 Price to Call Nper Pmt PV FV 10 $40 ($850.00) $1,075 7 8 Yield to Call Rate 6.65% 9 10 11 Formula RATE C3,C4,C5, C6)

Now Annual Yield to Call = 6.65% * 2 = 13.30%

(iii)

11 12 (1) 13 14 Time to Maturity 15 Coupon payment 16 Price 17 Face Value 18 19 Yield to Maturity 20 21 Nper Pmt PV FV 50 $40 ($850.00) $1,000 Rate 4.80% Formula RATE(C14,C15,C16,C17)

Now Annual Yield to Maturity = 4.80% * 2 = 9.60%

Now Highest Yield is Yield to Call

Lowest Yield is Yield to Maturity

To Value the Bond we use Yield to Maturity

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