Consider the following two mutually exclusive projects:

Net Cash Flow

End of Year Project A Project B
0 -$1000 -$1000
1 $912 $284
2 $684 $568
3 $456 $852
4 $228 $1136

At an interest rate of 25%, which project would you recommend choosing?

(Justify your answer using formulas and numbers on the calculation sheet/ You can use NPW, NAW or NFW for your analysis)

Question

Consider the following two mutually exclusive projects:

Net Cash Flow

End of Year	Project A	Project B
0	-$1000	-$1000
1	$912	$284
2	$684	$568
3	$456	$852
4	$228	$1136

At an interest rate of 25%, which project would you recommend choosing?

(Justify your answer using formulas and numbers on the calculation sheet/ You can use NPW, NAW or NFW for your analysis)

BlackTom AI · Accepted Answer

We start by restating the scenario and the two mutually exclusive projects with their cash flows and the given discount rate of 25%.

Question restatement:
- Projects: A and B
- Cash flows (End of Year):
  Year 0: A = -1000, B = -1000
  Year 1: A = 912,  B = 284
  Year 2: A = 684,  B = 568
  Year 3: A = 456,  B = 852
  Year 4: A = 228,  B = 1136
- Discount rate: r = 25%
- Objective: determine which project yields a higher net present worth (NPW/NPV) at r = 25% (you can use NPW, NAW, or NFW).

Option analysis (conceptual, since the provided answer list contains only one explicit option):
- Option 1: Choose Project A
  To evaluate, compute the net present value of Project A by discounting all future cash inflows at 25% and subtracting the initial investment. The present value of each inflow is:
  PV1(A) = 912 / 1.25 ≈ 729.60
  PV2(A) = 684 / (1.25)^2 ≈ 684 / 1.5625 ≈ 437.76
  PV3(A) = 456 / (1.25)^3 ≈ 456 / 1.953125 ≈ 233.50
  PV4(A) = 228 / (1.25)^4 ≈ 228 / 2.44140625 ≈ 93.40
  Sum of inflows PV ≈ 729.60 + 437.76 + 233.50 + 93.40 ≈ 1494.26
  NPW_A = Sum PV - Initial investment = 1494.26 − 1000 ≈ 494.26
  So, Project A has NPW ≈ +494.3 (positive and substantial).

- Option 2: Choose Project B
  Similarly, discount the inflows for Project B:
  PV1(B) = 284 / 1.25 = 227.20
  PV2(B) = 568 / (1.25)^2 ≈ 568 / 1.5625 ≈ 363.52
  PV3(B) = 852 / (1.25)^3 ≈ 852 / 1.953125 ≈ 436.20
  PV4(B) = 1136 / (1.25)^4 ≈ 1136 / 2.44140625 ≈ 465.50
  Sum PV ≈ 227.20 + 363.52 + 436.20 + 465.50 ≈ 1492.42
  NPW_B = 1492.42 − 1000 ≈ 492.42
  So, Project B has NPW ≈ +492.4.

Comparison and interpretation:
- Both projects have positive NPW at r = 25%, meaning each is financially acceptable on its own. However, since the projects are mutually exclusive, we compare their NPWs to choose the better option.
- NPW_A ≈ 494.3 is slightly higher than NPW_B ≈ 492.4, so Project A yields the larger net present value and is the preferable choice under the NPW criterion.

Why this conclusion makes sense conceptually:
- Discounting converts future cash inflows to their value today, accounting for the opportunity cost of capital at 25%. Higher NPW indicates greater value added by the project when considering the time value of money.
- The initial outlay is the same for both projects, so the comparison hinges on the timing and magnitude of the inflows. Project A provides larger or similarly-timed inflows in aggregate present value than Project B, leading to a higher NPW.

Why you might consider alternative interpretations (and why they align here):
- If you were to use the NAW (annual worth) approach, you would convert the net cash flows into an equivalent annual annuity and compare those amounts; given the NPW results, Project A would typically also yield a slightly higher annual worth.
- If you used the NFW (future worth) approach, you'd accumulate inflows to the end of the project horizon; although both projects end with positive future value, the earlier discounting effects at 25% still favor Project A by delivering a marginally higher present value, which translates to a higher future value when projected forward by the remaining years under the same rate.

Edge case note:
- The numerical difference between NPW_A and NPW_B is small (roughly 2 dollars in the present value difference in the approximated calculations), so if there were rounding or slight variation in the discount factor application, the ranking could become sensitive. In this calculation, A remains marginally superior.

In summary, evaluating the two options at 25% using NPW shows Project A providing the higher net present value, so selecting Project A is the more financially advantageous choice under these assumptions.

ENG 106 A01 WQ 2025 Homework #4

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