Can someone please breakdown this practice problem?
Janet has set a 7% yield as the goal for the bond portion of her portfolio. To achieve this goal, she has purchased a 7%, 15-year corporate bond at a discount price of 93.50. What amount of reinvestment income will she need to earn over this 15-year period to achieve a compound return of 7% on a semiannual basis?
A step at a time.
Step 1: If you invest 93.50 today at 7% (nominal, compounded semiannually), how much will you have in 15 years?
Ok Great
N - 30
PV - 935
I/Y - 3.5
PMT - 0
FV = 2,624.35
Step 2: How much of that future value will be principal?
1000 right
Yup.
Step 3: How much of that future value is coupons plus interest on coupons?
2624.35 - 1000 = 1624.35
FV = 1624
N = 30
PMT = 0
I/Y = 3.5
PV = 578.59
Would that be it?
You’re getting ahead of the program.
That’s correct.
Step 4: What is the total value of the coupon payments?
Ok - aren’t PMT’s set at 0?
You bought a bond. Are the coupon payments zero?
No - I ask b/c the value used for PMT was 0 - how is that the case?
Step 1 was asking what the future value would be of an investment of 935 invested at 7%, which you correctly solved to be 2,624.35. If Janet invests 935 today, never adds any money to the account, and never takes any money from the account, then the ending value of the account will need to be 2,624.35 for her to have earned a 7% return.
Now we’re trying to break that 2,624.35 ending value into pieces:
So . . . Step 4: What is the total value of the coupon payments?
Got it ok great
so would the TV of CPN pmts be 1624.35 - 935 = 689.35
No.
Let’s break it down further:
Step 4a: How much is a single coupon payment?
$35 per semi-annual pmt right?
Yup.
Step 4b: How many coupon payments will you receive?
Wouldn’t the FV be par value @ maturity? It’s a 15 year bond
Only if you remove the coupon payments and reinvestment income from the account.
Even then, at maturity you’ll get par plus one coupon, not just par.
What’s the answer to step 4b?
Magician can be persuasive. Don’t give up on him.
The key here is that it’s now 15 years later and there is a pot of cash of $2,624.35. And there were 3 sources of cash inflows to get Janet that big jackpot!!