Apa Cómo Citar

7. You have been offered a 7-year investment at a price of $50,000. It will pay $5,000 at the end of year 1, $10,000 at the end of year 2, and $15,000 at theend of year 3, plus a fixed but currently unspecified cash flow, X, at the end of Years 4 through 7. The payer is essentially riskless, so you are sure thepayments will be made, and you regard 9% as an appropriate rate of return on riskless 7-year investments. What cash flow must the investment provide at the end of each ofthe final 4 years, that is, what is X?

Time Line:
0 1 2 3 4 5 6 7|--------|--------|--------|--------|--------|--------|--------|
5,000 10,000 15,000 X X X X

We know that the present value ofall of these 7 cash flows today (at period 0) is $50,000. Then, start with calculating the present value of the known cash flows:

PV =
PV = $5,000 × 0.9174 +$10,000 × 0.8340 + $15,000 × 0.7582
PV = $4,587.1560 + $8,340.2836 + $11,373.1140 = $24,300.5536

Of course, you can also enter these into the cash flow registerof your financial calculator to calculate their present value, as was done in class.

Then, the present value, as of period 0, of all the four $X payments shouldbe:

$50,000 - $24,300.5536 = $25,699.4464

The four $X payments constitute an annuity that begins at period 3. The PV of this annuity as of period 3 is:

PVA=
The present value of this annuity as of period 0 is:
PV = FV
We know that this present value is equal to $25,699.4464:

$2.5325X = $25,699.4464

X =