P inc. is issuing annual pay bond that will pay no coupon for the first 5 years and then pay 10% coupon for the remanining 5 years until maturity. The int rate for the first five years will all be paid without additional int at maturity. if annual YTM is 10% the price of the bond per $ 1000 of face value is closest to:
2)$814
3)$856
Kindly explain how did you arrive at the solution
PMT=100; I/Y=10%; N=5; PV=0, solve for FV=610,51
1,000 + 1,000 x 0.1 x 5 = 1,500
PMT=0; I/Y=10%; N=10; FY=2,110.51, solve for PV=813.69 ~ $814
So answer 2 should be the correct one. Remember: there are no cash flows to be considered in the first 5 years. Best thing is to draw a timeline with the corresponding cash flows in each year. Otherwise this will look more difficult than it actually is.
Best, Oscar
Are you sure the question is right? Because If I solve it as it says, I would do the following:
1 2 3 4 5 6 7 8 9 10
0 , 0 , 0 , 0 , 0 , 100 , 100 , 100 , 100 , 1100
They NPV is 620.92 but there is no answer for it.
But reading well your question it says “the interest rate for the first 5 years will be paid without additional interest at maturity”, so I guess that the 5 first coupons will be paid also with the 5 last coupons, so remake the cash flow as follows:
1 2 3 4 5 6 7 8 9 10
0 , 0 , 0 , 0 , 0 , 200 , 200 , 200 , 200 , 1200
And the NPV is 856.3 which would be answer C.
Hope it helps,
Regards
As I understand it the interest from year 1 to 5 is accrued and paid at maturity in year 10 as I outlined in step 2 of my calculation. It explicitly says at maturity, so I assume it will be paid together with the principal in year 10.
Oscar is right, my bad. Didn’t understand the accrued interest which will be paid at maturity only.
So would be like calculating my first cash flow and getting a Price of 620.92 and discounting the 1000 x 0.1 x 5 = 500 interest accrued for 10 years would give a NPV of 192.8
620.92 + 192.77 = 813.69
Correct answer B
Regards
Yep, you right. We know now that his question had a common mistake option lol.
Thanks!