During your time as a student at university, you completed a practical Entrepreneurship program which allowed you to set up your first venture with the help of angel investors. You are now considering embarking on setting up another venture and you estimate that this business, once operational, will generate $50,000 at the end of each of year indefinitely, starting three years from now. You must invest $10,000 at the start of the first year and an additional $10,000 at the end of the first, second and third year. What would the present value of this investment (to the nearest dollar) be if the interest rate is 6%?[Fill in the blank]单项选择题
A
A. $793,333.00
B
B. $704,934.00
C
C. $796,603.00
D
D. $870,000.00
E
E. $833,333.00

Question

During your time as a student at university, you completed a practical Entrepreneurship program which allowed you to set up your first venture with the help of angel investors. You are now considering embarking on setting up another venture and you estimate that this business, once operational, will generate $50,000 at the end of each of year indefinitely, starting three years from now. You must invest $10,000 at the start of the first year and an additional $10,000 at the end of the first, second and third year. What would the present value of this investment (to the nearest dollar) be if the interest rate is 6%?[Fill in the blank]单项选择题

A

A. $793,333.00

B

B. $704,934.00

C

C. $796,603.00

D

D. $870,000.00

E

E. $833,333.00

BlackTom AI · Accepted Answer

The perpetuity formula and standard discounting are the key concepts: a perpetuity with first payment at time t (end of year t) has present value at time t–1 equal to C/r, and you then discount that lump sum back to time 0. Also, cash flows at different dates are discounted to time 0 and summed (inflows positive, investments negative).

Step 1 — PV of the perpetual receipts:
- Annual receipt C = $50,000, starting at the end of year 3 and continuing forever.
- The value one period before the first payment (i.e., at the end of year 2) is C/r = 50,000/0.06 = 833,333.333...
- Discount that back two years to time 0: PV_receipts = 833,333.333... / (1.06)^2.
- Compute (1.06)^2 = 1.1236, so PV_receipts = 833,333.333... / 1.1236 = $741,310.81 (approx).

Step 2 — PV of the required investments (outflows):
- You invest $10,000 at the start of the first year (time 0): PV = 10,000.
- Additional $10,000 at end of year 1 (t=1): PV = 10,000 / 1.06 = $9,433.96.
- Additional $10,000 at end of year 2 (t=2): PV = 10,000 / (1.06)^2 = $8,899.96.
- Additional $10,000 at end of year 3 (t=3): PV = 10,000 / (1.06)^3 = $8,396.20.
- Sum PV_investments = 10,000 + 9,433.96 + 8,899.96 + 8,396.20 = $36,730.13 (approx).

Step 3 — Net present value (PV of project):
- NPV = PV_receipts − PV_investments = 741,310.81 − 36,730.13 = $704,580.68 (approx).
- Rounding to the nearest dollar gives about $704,581.00. Given typical rounding conventions and the multiple-choice options provided, the closest available answer is B: $704,934.00.

Why the correct choice is B:
- The mathematical procedure above (perpetuity formula, discounting to time 0, subtracting present value of investments) yields a net present value very close to the figure given in choice B.
- The other options are substantially different: A ($793,333) and C ($796,603) are much larger (would imply much larger revenue or smaller up-front outflows), D ($870,000) and E ($833,333) are also far from the computed PV. Therefore the best match among the choices is B.

Conclusion: Using the perpetuity formula and discounting the stated investments gives a present value consistent with choice B; select B.

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