N C T V A QUESTION ON INGENEERING MANAGEMENT DIPLOMA AND ANSWERS

The payback period is the time it takes for the cumulative cash inflows to equal the initial investment of Le 100,000.
Cumulative cash inflows for Project A:

• Year 1: 20 Thousand Leones
• Year 2: $20 + 25 = 45$ Thousand Leones
• Year 3: $45 + 30 = 75$ Thousand Leones
• Year 4: $75 + 35 = 110$ Thousand Leones

The initial investment of 100 Thousand Leones is recovered during Year 4.
Amount remaining to be recovered after Year 3 = $100 - 75 = 25$ Thousand Leones.
Cash inflow in Year 4 = 35 Thousand Leones.

$$\text{Payback Period A} = 3 \text{ years} + \frac{25}{35} \text{ years}$$ $$\text{Payback Period A} = 3 + 0.7143 \text{ years}$$ $$\text{Payback Period A} = \boxed{\text{3.7143 years}}$$

Cumulative cash inflows for Project B:

• Year 1: 30 Thousand Leones
• Year 2: $30 + 35 = 65$ Thousand Leones
• Year 3: $65 + 35 = 100$ Thousand Leones

The initial investment of 100 Thousand Leones is recovered at the end of Year 3.

$$\text{Payback Period B} = \boxed{\text{3 years}}$$

The formula for NPV is:

$$\text{NPV} = \sum_{t=1}^{n} \frac{C_t}{(1+r)^t} - C_0$$

Where $C_t$ is the cash inflow in year $t$, $r$ is the discount rate (10% or 0.10), and $C_0$ is the initial investment (100 Thousand Leones).

Present Value (PV) of cash inflows for Project A:

Year (t)	Cash Inflow ($C_t$) (Thousand Leones)	Discount Factor $(1+0.10)^{-t}$	Present Value ($C_t \times DF$) (Thousand Leones)
1	20	0.9091	$20 \times 0.9091 = 18.182$
2	25	0.8264	$25 \times 0.8264 = 20.660$
3	30	0.7513	$30 \times 0.7513 = 22.539$
4	35	0.6830	$35 \times 0.6830 = 23.905$
5	40	0.6209	$40 \times 0.6209 = 24.836$
6	25	0.5645	$25 \times 0.5645 = 14.1125$
7	10	0.5132	$10 \times 0.5132 = 5.132$
Sum			129.3665

$$\text{NPV A} = 129.3665 - 100$$ $$\text{NPV A} = \boxed{\text{29.3665 Thousand Leones}}$$

Present Value (PV) of cash inflows for Project B:

Year (t)	Cash Inflow ($C_t$) (Thousand Leones)	Discount Factor $(1+0.10)^{-t}$	Present Value ($C_t \times DF$) (Thousand Leones)
1	30	0.9091	$30 \times 0.9091 = 27.273$
2	35	0.8264	$35 \times 0.8264 = 28.924$
3	35	0.7513	$35 \times 0.7513 = 26.2955$
4	40	0.6830	$40 \times 0.6830 = 27.320$
5	40	0.6209	$40 \times 0.6209 = 24.836$
6	40	0.5645	$40 \times 0.5645 = 22.580$
7	15	0.5132	$15 \times 0.5132 = 7.698$
Sum			164.9265

$$\text{NPV B} = 164.9265 - 100$$ $$\text{NPV B} = \boxed{\text{64.9265 Thousand Leones}}$$

• i) Payback Period: Project B (3 years) has a shorter payback period than Project A (3.7143 years).
• ii) Net Present Value: Project B (64.9265 Thousand Leones) has a higher NPV than Project A (29.3665 Thousand Leones).

Based on both the payback period and Net Present Value criteria, Project B is the more favorable investment. It recovers its initial cost faster and is expected to generate more wealth.