Principles of Finance Practice Question

[iowa43]

I'm having trouble determining how to find the answer for this question. Any help would be appreciated. Thanks in advance!

"A bond with a par value of $1,000, a coupon rate of 5%, 3 years to maturity, and making annual payments, is worth how much if the current discount rate is 7%?"

The correct answer is $947.51. The answer key says to use the NPV equation.

[islandcoli]

For this type of question you must have the PV formula memorized. PV = FV / (1+r)n

Fundamentally NPV allows us to compare any two investments and determine which is the better investment.

Let's go thru the terms the problem gives us one by one.

Par Value is the original investment sometimes referred to as principle. In this case it is 1,000 because that information is given to us.

Coupon rate is the payment you receive each term (in this case annually/you will receive 3 payments over 3 years)
We know the coupon rate is 5% because that info is provided.
So 5% of 1,000 is 50.
So 50 in year one, 50 in year 2, 50 in year 3.
(A good way to remember what the coupon is, is to think about bonds in the old days.. In the old days you would literally have a piece a paper and once a term you would physically TEAR the "coupon" off your paper-bond and present it to for payment. At the end of the bonds term(maturity) you would have no more coupons left to tear.)

Annual is YEARLY. (this test will use Annual/Biannual and semiannual.. know those terms)

Maturity is just a fancy way of saying when it ends. Maturity of 3 years is a bond that is completed in 3 years.

First we need to find the PRESENT VALUE of each year. We do this by applying the PV formula individually to each year individually. YEAR BY YEAR.
Using the Present Value formula which is "PV = FV / (1+r)n" another way to say it is "COUPON PAYMENT FOR THAT YEAR ÷ 1.07 to the power of whatever year we are in E.G 1,2,3
The reason it's 1.07 is because the rate is 7% which in a decimal is represented as .07 --> 1+.07 = 1.07

Year One = $50 / (1.07) to the 1st power = 46.72
Year Two = $50 / (1.07) to the 2nd power = 43.67
Year Three = $1050 / (1.07) to the 3rd power = 857.11 <--- we are including the original 1,000 because in the final year(maturity) the original amount is returned

46.72 + 43.67 + 857.11 = $947.51

So now we take that number and add it back. Remember that when we invest in a bond we represent it as a negative number (since we gave up our money at the time)

we invested -1000 at the start

-1000 + 947.51 = -52.49

If on the test it asks if you would take this investment; the answer would be no because we have a negative number -52.49.

Tip: As far as this test is concerned you never take a negative NPV and always take a positive NPV

I will try and update this thread with a video as I'm having trouble transcribing my thoughts to text.


EDIT: https://www.youtube.com/watch?v=jylJ2r9bklE

Try that video. Keep in mind for this problem in year 3 the "payment" includes your principles.

[iowa43]

Thank you so much for your explanation and for finding that video. I appreciate your time!

[clep3705]

Once you understand the solution, you should be able to answer this question: If interest rates rise, what happens to the value of the bond?