(a) The Net Discount Value, commonly referred to as Net Present Value (NPV), is a financial metric used in capital budgeting to evaluate the profitability of an investment project. It represents the difference between the present value of all future cash inflows generated by the project and the present value of the initial investment and any other cash outflows. The calculation accounts for the time value of money by discounting future cash flows back to their present value using a specified discount rate, which in this case is 14% per annum reflecting the opportunity cost of capital for similar projects in the banking sector.

In relation to these projects, a positive NPV indicates that the project is expected to generate returns above the required rate, adding value to the bank. A negative NPV suggests the opposite. NPV helps in decision-making by allowing comparison between proposals; the one with the higher NPV is generally preferred, assuming other factors like risk and liquidity are comparable. This aligns with Ghanaian banking practices under BoG guidelines, where investment decisions must ensure profitability and compliance with capital adequacy requirements post the 2017-2019 banking cleanup.

(b) To calculate the Net Discounted Value (NPV) for Proposal A:

The formula for NPV is:

NPV=−C0+∑t=1nCt(1+r)t NPV = -C_0 + \sum_{t=1}^{n} \frac{C_t}{(1 + r)^t} NPV=−C0​+∑t=1n​(1+r)tCt​​

Where:

• C0 C_0 C0​ = Initial investment = GHS 80,000
• Ct C_t Ct​ = Net cash inflow in year t
• r = Discount rate = 14% or 0.14
• n = Number of years = 3

Cash flows:

• Year 1 (1991): GHS 95,400
• Year 2 (1992): GHS 39,400
• Year 3 (1993): GHS 12,000

Step-by-step calculation:

1. Present value of Year 1 cash flow: 95,4001.14=83,684.21 \frac{95,400}{1.14} = 83,684.21 1.1495,400​=83,684.21
2. Present value of Year 2 cash flow: 39,4001.142=39,4001.2996=30,317.05 \frac{39,400}{1.14^2} = \frac{39,400}{1.2996} = 30,317.05 1.14239,400​=1.299639,400​=30,317.05
3. Present value of Year 3 cash flow: 12,0001.143=12,0001.481544=8,099.63 \frac{12,000}{1.14^3} = \frac{12,000}{1.481544} = 8,099.63 1.14312,000​=1.48154412,000​=8,099.63
4. Sum of present values: 83,684.21 + 30,317.05 + 8,099.63 = 122,100.89
5. NPV = Sum of PVs – Initial investment = 122,100.89 – 80,000 = GHS 42,100.89

Thus, the NPV for Proposal A is GHS 42,100.89.

(c) To calculate the Net Discounted Value (NPV) for Proposal B:

Using the same formula:

Initial investment C0 C_0 C0​ = GHS 100,000

Cash flows:

• Year 1: GHS 35,000
• Year 2: GHS 58,000
• Year 3: GHS 80,000

Step-by-step calculation:

1. Present value of Year 1 cash flow: 35,0001.14=30,701.75 \35,000} {1.14} = 30,701.75 1.1435,000​=30,701.75
2. Present value of Year 2 cash flow: 58,0001.142=58,0001.2996=44,629.12 \frac{58,000}{1.14^2} = \58,000} {1.2996} = 44,629.12 1.14258,000​=1.299658,000​=44,629.12
3. Present value of Year 3 cash flow: 80,0001.143=80,0001.481544=53,997.72 \80,000} {1.14^3} = \80,000} {1.481544} = 53,997.72 1.14380,000​=1.48154480,000​=53,997.72
4. Sum of present values: 30,701.75 + 44,629.12 + 53,997.72 = 129,328.59
5. NPV = 129,328.59 – 100,000 = GHS 29,328.59

Thus, the NPV for Proposal B is GHS 29,328.59.

(d) Based on the calculated NPVs, Proposal A has a higher NPV (GHS 42,100.89) compared to Proposal B (GHS 29,328.59). Therefore, Management should select Proposal A, as it is expected to add more value to the Rural Bank. This decision supports profitability and aligns with BoG’s emphasis on efficient capital allocation for sustainable banking operations in Ghana. However, consider qualitative factors such as risk exposure, liquidity needs under the Liquidity Risk Management Guidelines, and alignment with post-DDEP recovery strategies to ensure resilience.