Net present Value

Question

Assume that the management team of png taiheyo ltd woukd like to compare investment in the rock crusher from komatsu over the time period of 10 years with discount rates of 10% and 5%. The cost of the crusher is estimated at K1250000. The cash inflow for the crusher is assumed to be K500000 annually over 10 years. At the end of the 10th year, the crushers value are estimated to be zero after taking into account the depreciation expense at 20% straight line for the duration of the cash flows. The management team has asked to see the net present value of the crusher at 10% and 5% discount saperately.
A) calculate the NPV of the cashflow at 10%.
B) Calculate the NPV of the cash flow at 5%.
C) what wojld be your advice to the management yeam after you have calculated the net present value of the Komatsu rosk crusher at 10% and 5% discount rates?

Answer 1

To calculate the Net Present Value (NPV) for the cash inflows from the Komatsu rock crusher, we will use the formula for NPV, which is given by:

\[ NPV = \sum \frac{C_t}{(1 + r)^t} - C_0 \]

Where:

• \( C_t \) = cash inflow during the period \( t \)
• \( r \) = discount rate (10% or 5%)
• \( t \) = year
• \( C_0 \) = initial investment

Given Information:

• Initial Cost of Crusher, \( C_0 = K1,250,000 \)
• Annual Cash Inflow, \( C_t = K500,000 \)
• Duration, \( t = 10 \) years

A) Calculate the NPV of the cash flow at 10%

Using a discount rate of 10%:

\[ NPV = \sum_{t=1}^{10} \frac{K500,000}{(1+0.10)^t} - K1,250,000 \]

Calculating the present value of each cash inflow:

\[ PV = K500,000 \left( \frac{1 - (1 + 0.10)^{-10}}{0.10} \right) \]

Using the formula for the present value of an annuity:

\[ PV = K500,000 \left( \frac{1 - (1 + 0.10)^{-10}}{0.10} \right) = K500,000 \times 5.6446 \approx K2,822,300 \]

Now, calculate NPV:

\[ NPV = K2,822,300 - K1,250,000 = K1,572,300 \]

B) Calculate the NPV of the cash flow at 5%

Using a discount rate of 5%:

\[ NPV = \sum_{t=1}^{10} \frac{K500,000}{(1+0.05)^t} - K1,250,000 \]

Calculating the present value of each cash inflow similarly:

\[ PV = K500,000 \left( \frac{1 - (1 + 0.05)^{-10}}{0.05} \right) \]

Using the present value of an annuity formula again:

\[ PV = K500,000 \left( \frac{1 - (1 + 0.05)^{-10}}{0.05} \right) = K500,000 \times 7.7217 \approx K3,860,850 \]

Now, calculate NPV:

\[ NPV = K3,860,850 - K1,250,000 = K2,610,850 \]

C) Advice to the Management Team

Based on the calculated NPVs:

• NPV at 10% discount rate = K1,572,300
• NPV at 5% discount rate = K2,610,850

Recommendation:

Both NPVs are positive, indicating that the investment in the Komatsu rock crusher is expected to generate more cash inflows than the initial cost, thus creating value for the company. However, the NPV is significantly higher at the 5% discount rate compared to the 10% discount rate.

• If the management's required rate of return is below 10%, the crusher is a good investment since it produces a positive NPV.
• If the required rate of return is above 10%, the decision may be reconsidered since the attractiveness of the investment diminishes.

Overall, if the company can afford to take on this investment without exceeding any thresholds for risk and if the projected cash flows hold true, it could be a beneficial investment at either discount rate.