Hello,
I have been going over this question for hours now and I so frustrated. I hope someone here can help tell me what I am doing wrong.
The question in this study guide is:
“To finance part of an owner’s new manufacturing facility, the board of directors decides to issue 2,000 bonds with a face value of $1,000, all of which are due in 15 years. The bond coupons shall pay 8% annum, and the coupons are payable semiannually. If buyers expect a compounded 10% rate-of-return on their investment, what should they pay for the bonds?”
A: $847.89
B: $854.30
C: $930.10
D $943.52
So, I tried to use the bond function in the calculator, but I know that the payment is basically $40.00 twice a year off the bond for 15 years. So then I tried to type it the calculator as:
Which is NONE of the answers. I know this should be a positive # - maybe the PMT of $40 should go in as -$40. I am more concerned with that I am obviously missing a step or something. I tried to set the calculator to BGN and that didn’t work. IDK WTH. HELP!! The book says the answer is B: $854.30
Excuse my ignorance but I am not sure where I would find that. I am guessing you mean an error in the study guide. I have completed a few questions, and they are all a few dollars off here and there. The only thing I can think of is the answers are written out like you would figure it out without a financial calculator - but I would (hope) I would get the same answers… but I am not. This one the answer was written out like this -
A bond buyer expecting a 10% rate of return will pay $854.30 today in exchange of a bond for $1,000 received at the end of 15 years and thirty $40 payments received semi-annually. Note: Since coupons are payable semi-annually, the compound interest factor will be treated as n = 15*2 = 30 but discounted at half of the desired rate of return (5%=10%/2)
The question is written really poorly and the soilution is inconsistent in its use of interest rates
The convention, unless explicitly stated otherwise, is the yield is quoted with teh same periodicity as the payment of the coupons. So semi-annual payments means 10% is a nominal rate with semi annual compounding. i.e. 5% per 6 month period.
To me compounded 10% rate-of-return on their investment implies an effective annual rate of 10% or 4.881% for 6 months [ 1.1^(1/2) - 1 = 0.04881], but I realise that might be just my interpretation.
Either way the answer is wrong as they have used a 5% per 6 months rate for the coupons.
but 10% rate for the 1000 par value.
It be consistent with coupons it should be 10.25% (1.05^2 - 1 = 0.1)
Using there answer convention the answer should be
If we have 10% as a nominal rate (5% per 6 months)
(obviously TVM keys best but this is to use solutions convention to highlight error)
Annuity Coupons = 614.90
Par value = 231.28
Total = 846.28
If we have 10% as a effective annual rate (4.881% per 6 months)
Annuity Coupons = 623.24
Par value = 239.39
Total = 862.73
The solution provided does
Annuity Coupons = 614.90 (discounted at 5% per 6 months)
Par value = 239.39 (discounted at 4.88% per 6 months, 10% per annum)
