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- You both decided to finance the project using your own funds. - The cost of t...
Aug 13, 2024
Solution by Steps
step 1
To calculate the NPV using your partner's optimistic estimates, we first determine the cash inflows for each year: RM60,000 for 6 years and RM50,000 from the sale of equipment at the end of Year 6. The formula for NPV is given by: NPV=∑t=1nCt(1+r)t−C0 NPV = \sum_{t=1}^{n} \frac{C_t}{(1+r)^t} - C_0 where CtC_t is the cash inflow at time tt, rr is the discount rate, and C0C_0 is the initial investment. Here, r=0.05r = 0.05 and C0=200,000C_0 = 200,000
step 2
For the optimistic estimates, the cash flows are: - Year 1: RM60,000 - Year 2: RM60,000 - Year 3: RM60,000 - Year 4: RM60,000 - Year 5: RM60,000 - Year 6: RM60,000 + RM50,000 (salvage value) = RM110,000. Now, we calculate the NPV: NPV=60,000(1+0.05)1+60,000(1+0.05)2+60,000(1+0.05)3+60,000(1+0.05)4+60,000(1+0.05)5+110,000(1+0.05)6−200,000 NPV = \frac{60,000}{(1+0.05)^1} + \frac{60,000}{(1+0.05)^2} + \frac{60,000}{(1+0.05)^3} + \frac{60,000}{(1+0.05)^4} + \frac{60,000}{(1+0.05)^5} + \frac{110,000}{(1+0.05)^6} - 200,000
step 3
Calculating each term: - Year 1: 60,0001.05≈57,142.86 \frac{60,000}{1.05} \approx 57,142.86 - Year 2: 60,000(1.05)2≈54,421.78 \frac{60,000}{(1.05)^2} \approx 54,421.78 - Year 3: 60,000(1.05)3≈51,843.09 \frac{60,000}{(1.05)^3} \approx 51,843.09 - Year 4: 60,000(1.05)4≈49,305.80 \frac{60,000}{(1.05)^4} \approx 49,305.80 - Year 5: 60,000(1.05)5≈46,809.05 \frac{60,000}{(1.05)^5} \approx 46,809.05 - Year 6: 110,000(1.05)6≈82,700.00 \frac{110,000}{(1.05)^6} \approx 82,700.00 Now, summing these values gives us the total present value of cash inflows
step 4
The total present value of cash inflows is approximately: 57,142.86+54,421.78+51,843.09+49,305.80+46,809.05+82,700.00≈342,222.58 57,142.86 + 54,421.78 + 51,843.09 + 49,305.80 + 46,809.05 + 82,700.00 \approx 342,222.58 Now, we calculate the NPV: NPV=342,222.58−200,000≈142,222.58 NPV = 342,222.58 - 200,000 \approx 142,222.58
step 5
Now, we calculate the NPV using your cautious estimates. The cash flows are: - Year 1: RM40,000 - Year 2: RM50,000 - Year 3: RM60,000 - Year 4: RM70,000 - Year 5: RM80,000 - Year 6: RM80,000 + RM50,000 (salvage value) = RM130,000. Using the same NPV formula, we calculate: NPV=40,000(1+0.05)1+50,000(1+0.05)2+60,000(1+0.05)3+70,000(1+0.05)4+80,000(1+0.05)5+130,000(1+0.05)6−200,000 NPV = \frac{40,000}{(1+0.05)^1} + \frac{50,000}{(1+0.05)^2} + \frac{60,000}{(1+0.05)^3} + \frac{70,000}{(1+0.05)^4} + \frac{80,000}{(1+0.05)^5} + \frac{130,000}{(1+0.05)^6} - 200,000
step 6
Calculating each term for cautious estimates: - Year 1: 40,0001.05≈38,095.24 \frac{40,000}{1.05} \approx 38,095.24 - Year 2: 50,000(1.05)2≈45,351.56 \frac{50,000}{(1.05)^2} \approx 45,351.56 - Year 3: 60,000(1.05)3≈51,843.09 \frac{60,000}{(1.05)^3} \approx 51,843.09 - Year 4: 70,000(1.05)4≈57,305.80 \frac{70,000}{(1.05)^4} \approx 57,305.80 - Year 5: 80,000(1.05)5≈62,809.05 \frac{80,000}{(1.05)^5} \approx 62,809.05 - Year 6: 130,000(1.05)6≈100,000.00 \frac{130,000}{(1.05)^6} \approx 100,000.00 Now, summing these values gives us the total present value of cash inflows
step 7
The total present value of cash inflows for cautious estimates is approximately: 38,095.24+45,351.56+51,843.09+57,305.80+62,809.05+100,000.00≈355,404.74 38,095.24 + 45,351.56 + 51,843.09 + 57,305.80 + 62,809.05 + 100,000.00 \approx 355,404.74 Now, we calculate the NPV: NPV=355,404.74−200,000≈155,404.74 NPV = 355,404.74 - 200,000 \approx 155,404.74
Answer
For the optimistic estimates, NPV ≈ RM142,222.58; for the cautious estimates, NPV ≈ RM155,404.74.
Key Concept
Net Present Value (NPV) is a method used to evaluate the profitability of an investment by comparing the present value of cash inflows to the initial investment.
Explanation
The NPV values indicate that both estimates are positive, suggesting financial viability, but the cautious estimates yield a higher NPV, making them more favorable for the project's financial viability.
(ii) Interpretation of NPV Values
The optimistic estimate yields an NPV of RM142,222.58, while the cautious estimate yields RM155,404.74. The higher NPV from the cautious estimate suggests it is more favorable for the project's financial viability.
(iii) Impact of Cash Flow Variations
Variations in cash flow patterns can significantly impact investment decisions, as they affect the NPV and overall financial assessment of a project. More stable and predictable cash flows generally lead to more favorable investment evaluations.
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