Require: a) Which of the source pay its way earliest? b) Suppose the current cost of borrowing in the capital market is 25% and 30%. What is the internal rate of return (IRR) on each source of the loan and advice the GM accordingly?

Here's the solution to your question:

Part a) Which of the source pays its way earliest?

To determine which source pays its way earliest, we calculate the payback period for each. The payback period is the time it takes for the cumulative cash inflows to equal the initial investment.

• Step 1: Calculate Payback Period for BOND. Initial Investment = N120,000 Year 1 Cash Inflow = N50,000 Remaining amount to recover after Year 1 = N120,000 - N50,000 = N70,000 Year 2 Cash Inflow = N75,000 Since N70,000 is less than N75,000, the remaining amount will be recovered within Year 2. Fraction of Year 2 needed = $\frac{70,000}{75,000} \approx 0.9333$ years Payback Period for BOND = $1 \text{ year} + 0.9333 \text{ years} = 1.9333 \text{ years}$

• Step 2: Calculate Payback Period for BANK. Initial Investment = N130,000 Year 1 Cash Inflow = N90,000 Remaining amount to recover after Year 1 = N130,000 - N90,000 = N40,000 Year 2 Cash Inflow = N50,000 Since N40,000 is less than N50,000, the remaining amount will be recovered within Year 2. Fraction of Year 2 needed = $\frac{40,000}{50,000} = 0.8 \text{ years}$ Payback Period for BANK = $1 \text{ year} + 0.8 \text{ years} = 1.8 \text{ years}$

• Step 3: Compare Payback Periods. BOND Payback Period = 1.9333 years BANK Payback Period = 1.8 years Since 1.8 years < 1.9333 years, the BANK source pays its way earliest.

  The source that pays its way earliest is the BANK.

Part b) Calculate the Internal Rate of Return (IRR) on each source of the loan and advice the GM accordingly.

The Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value (NPV) of all cash flows equal to zero. We assume the initial amount loanable is the initial investment (outflow) and the anticipated cash inflows are the returns. The cost of borrowing for BOND is assumed to be 25% and for BANK is 30%, based on the phrasing "25% and 30%".

• Step 4: Calculate IRR for BOND. Cash flows: $CF_0 = -120,000$, $CF_1 = 50,000$, $CF_2 = 75,000$, $CF_3 = 80,000$. We need to find IRR such that:

  $$-120,000 + \frac{50,000}{(1+IRR)^1} + \frac{75,000}{(1+IRR)^2} + \frac{80,000}{(1+IRR)^3} = 0$$

  Using trial and error: At $IRR = 20\%$:

  $$NPV(20\%) = -120,000 + \frac{50,000}{1.20} + \frac{75,000}{(1.20)^2} + \frac{80,000}{(1.20)^3}$$ $$NPV(20\%) = -120,000 + 41,666.67 + 52,083.33 + 46,296.30 = 20,046.30$$

  At $IRR = 30\%$:

  $$NPV(30\%) = -120,000 + \frac{50,000}{1.30} + \frac{75,000}{(1.30)^2} + \frac{80,000}{(1.30)^3}$$ $$NPV(30\%) = -120,000 + 38,461.54 + 44,378.70 + 36,204.09 = -955.67$$

  Using interpolation:

  $$IRR = 0.20 + \frac{20,046.30}{20,046.30 - (-955.67)} (0.30 - 0.20)$$ $$IRR = 0.20 + \frac{20,046.30}{21,001.97} (0.10) \approx 0.20 + 0.09545 = 0.29545$$

  The IRR for BOND is approximately $29.55\%$.

• Step 5: Calculate IRR for BANK. Cash flows: $CF_0 = -130,000$, $CF_1 = 90,000$, $CF_2 = 50,000$, $CF_3 = 60,000$. We need to find IRR such that:

  $$-130,000 + \frac{90,000}{(1+IRR)^1} + \frac{50,000}{(1+IRR)^2} + \frac{60,000}{(1+IRR)^3} = 0$$

  Using trial and error: At $IRR = 25\%$:

  $$NPV(25\%) = -130,000 + \frac{90,000}{1.25} + \frac{50,000}{(1.25)^2} + \frac{60,000}{(1.25)^3}$$ $$NPV(25\%) = -130,000 + 72,000 + 32,000 + 30,720 = 4,720$$

  At $IRR = 30\%$:

  $$NPV(30\%) = -130,000 + \frac{90,000}{1.30} + \frac{50,000}{(1.30)^2} + \frac{60,000}{(1.30)^3}$$ $$NPV(30\%) = -130,000 + 69,230.77 + 29,585.80 + 27,153.07 = -4,030.36$$

  Using interpolation:

  $$IRR = 0.25 + \frac{4,720}{4,720 - (-4,030.36)} (0.30 - 0.25)$$ $$IRR = 0.25 + \frac{4,720}{8,750.36} (0.05) \approx 0.25 + 0.02697 = 0.27697$$

  The IRR for BANK is approximately $27.70\%$.

• Step 6: Advice to the GM. The problem states the current cost of borrowing in the capital market is 25% and 30%. We interpret this as the cost of borrowing for the BOND being 25% and for the BANK loan being 30%.

  For BOND:
  IRR = 29.55%
  Cost of borrowing = 25%
  Since $29.55\% > 25\%$, the BOND is an acceptable source of finance.

  For BANK:
  IRR = 27.70%
  Cost of borrowing = 30%
  Since $27.70\% < 30\%$, the BANK loan is not an acceptable source of finance.

  Given that these are mutually exclusive sources, the GM should choose the BOND.

The final answers are:

a) The source that pays its way earliest is the $\boxed{\text{BANK}}$.

b) The Internal Rate of Return (IRR) for BOND is approximately $\boxed{29.55\%}$ and for BANK is approximately $\boxed{27.70\%}$.
The GM should be advised to choose the $\boxed{\text{BOND}}$ as its IRR (29.55%) is greater than its cost of borrowing (25%), making it an acceptable and superior option compared to the BANK loan, whose IRR (27.70%) is less than its cost of borrowing (30%).