Question

Pinnacle Consulting is planning to issue a zero-coupon bond with a 5-year maturity at a yield to maturity of 1.95%. Pinnacle needs to raise $5,000,000. To the nearest thousand, how many bonds do they need to issue?

*a zero-coupon bond pays no coupon interest payments, but is still calculated as if they pay semi-annually* State your answer in dollars, e.g., 12,849,000 not 12,849

Answer 1

Face Value of Zero Coupon Bond = $1000

Semi-annual YTM = YTM/2 = 1.5%/2 (As it is been stated that as if they pay semi-annually coupon, so Taking YTM as semi-annually also)

= 0.975%

n = No of years to maturity*2 (Semi-annuallY)

= 5 years*2

= 10

Price of Zero Coupon Bond = Face Value/(1+Semi-annual YTM)^n

Price of Zero Coupon Bond = $1000/(1+0.00975)^10

= $1000/1.10189095575

Price of Zero Coupon Bond = $907.53

- Amount needs to be raise by Pinnacle = $5,000,000

No of Bonds needs to be raise = Amounts to be raise/Price of Zero-coupon Bond

= $5,000,000/$907.53

= 5509

So, To the nearest thousand, how many bonds do they need to issue is 6,000