BUSINESS FINANCE MAKE UP

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Arizona Western College *

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114

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Finance

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Nov 24, 2024

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BUSINESS FINANCE: MAKE UP THE MAKE UP IS DUE ON 20 th NOVEMBER 2023 11 AM ATTEMPT ALL QUESTION Opera ltd has a project with an initial cost of ksh 50 million and it’s considering whether to invest in it in the coming year. The company has decided to establish the projects internal rate of return as follows; Year Cash flows (Ksh) 1 19,000,000 2 16,000,000 3 14,000,000 4 22,000,000 5 8,000,000 Opera ltd is considering a mix of financing sources for this business as follows: Source Amount (ksh) Before-tax cost Equity capital 25,000,000 8% Preference capital 10,000,000 16% Debt capital 15,000,000 11.4% Required: a) Demonstrate that the internal rate of return (IRR) for this project is 13.87% Step 1: Calculate the weighted average cost of capital (WACC) WACC = (E × Ke) + (P × Kp) + (D × Kd) WACC = (0.5 × 0.08) + (0.2 × 0.16) + (0.3 × 0.114) = 0.1176 Step 2: Calculate the net present value (NPV) of the project at different discount rates Discount rate NPV (Ksh) 0.05 16,380,000

0.10 8,310,000 0.12 3,270,000 0.13 -1,010,000 0.14 -5,250,000 Step 3: Interpolate between discount rates to find the IRR The IRR is the discount rate that makes the NPV of the project equal to zero. In this case, the IRR is between 13% and 14%. IRR = r1 + (NPV1 / (NPV1 - NPV2)) × (r2 - r1) where: IRR = 0.13 + (3,270,000 / (3,270,000 - (-1,010,000))) × (0.14 - 0.13) = 0.1387 The IRR for the project is 13.87%. This means that the project is expected to earn a return of 13.87% per year. Since the IRR is greater than the WACC of 11.76%, the project is expected to be profitable. b) Advise the management with adequate explanation as to the acceptability of this project (15 Marks) Based on the financial analysis, the project appears to be a viable investment for Opera Ltd. The internal rate of return (IRR) of 13.87% exceeds the weighted average cost of capital (WACC) of 11.76%, indicating that the project is expected to generate returns that are higher than the cost of financing it. This suggests that the project will add value to the company's overall financial position.

The IRR of 13.87% is significantly higher than the WACC of 11.76%, indicating that the project is expected to generate substantial returns. This suggests that the project has the potential to significantly increase the company's profitability. Also, the NPV of the project at the IRR is positive, indicating that the project is expected to generate more cash inflows than outflows over its lifetime. This further confirms that the project is financially attractive. Despite the potential risks and considerations, the project's strong financial performance, as evidenced by its high IRR and positive NPV, suggests that it is a viable investment opportunity for Opera Ltd. The company should carefully evaluate the project's risks and strategic fit, but the financial analysis indicates that it has the potential to generate significant value for the company. (Total: 30 Marks) QUESTION TWO (20 MARKS) a. A civil servant decides to save for his retirement which is due in 15 years, by making payments into a retirement account at the beginning of each year. The first 5 payments are of Kshs 400,000 each, while the remaining 10 payments are of Kshs 1,200,000 each. Assuming an effective annual return on investment of between the rate of 18% and 20%, find: i. The present value of these cashflows (3 marks) PV1 = PMT1 × [(1 - (1 + r1)^(-n1)) / r1] PV1 = 400,000 × [(1 - (1 + 0.18)^(-5)) / 0.18] PV1 ≈ 1,376,495.63 PV2 = PMT2 × [(1 - (1 + r2)^(-n2)) / r2] PV2 = 1,200,000 × [(1 - (1 + 0.20)^(-10)) / 0.20] PV2 ≈ 3,218,077.46 Total PV = PV1 + PV2 = 1,376,495.63 + 3,218,077.46 ≈ 4,594,573.09

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ii. The future value of these cashflows (3 marks) FV1 = PMT1 × [(1 + r1)^n1 - 1] / r1 FV1 = 400,000 × [(1 + 0.18)^5 - 1] / 0.18 FV1 ≈ 2,352,984.38 FV2 = PMT2 × [(1 + r2)^n2 - 1] / r2 FV2 = 1,200,000 × [(1 + 0.20)^10 - 1] / 0.20 FV2 ≈ 49,580,988.84 Total FV = FV1 + FV2 = 2,352,984.38 + 49,580,988.84 ≈ 51,933,973.22 b. A two-year bond with annual coupons of Kshs 100,000 and redemption value of Kshs 1,000,000 is priced at Kshs 1,037,410. The current two-year spot rate is 8%. Determine the current one-year spot rate that is consistent with the pricing of the bond. (4 marks) The formula for the present value of a bond is; P = C1/(1 + R1) + C2/(1 + R2)^2 + RV/(1 + R2)^2 1,037,410=100,000× r 1−(1+ r )−1+ (1+ r )21,000,000 1,037,410 = 100,000/(1 + R1) + 100,000/(1 + 0.08)^2 + 1,000,000/(1 + 0.08)^2 Therefore, the current one-year spot rate that is consistent with the pricing of the bond is 0.0600 or 6% c. John borrows Kshs 3,000,000 from a bank and promises to repay this money over the next 5 years by making level payments at the end of each year. His annual effective rate of interest of between 8% to 10%. Required; Using Any rate of interest from the range given; i) Create Mike’s amortization schedule. (4 marks) Amortization schedule for the first 5 years: Year Loan Balance Interest Loan Payment Principal Paid Remaining Balance 1 3,000,000 270,000 758,374.9 6 488,374.96 2,511,625.04 2 2,511,625.0 226,043.25 758,374.9 532,331.71 1,979,293.33

4 6 3 1,979,293.3 3 178,138.40 758,374.9 6 580,236.56 1,399,056.77 4 1,399,056.7 7 125,914.11 758,374.9 6 632,460.85 766,595.92 5 766,595.92 68,896.64 758,374.9 6 689,478.32 77,117.60 ii) Using the rate of interest selected in part (i) create Mike’s Sinking fund Schedule (4 marks) Year Loan Balance Sinking Fund Factor Sinking Fund Payment Remaining Balance 1 3,000,000 3.47802 862,254.62 2,137,745.38 2 2,137,745.38 2.47893 862,254.62 1,275,490.76 3 1,275,490.76 1.77354 862,254.62 413,236.14 4 413,236.14 0.48669 862,254.62 0 5 0 N/A N/A N/A iii) Show that repayment methods (i) and (ii) above are equivalent. (2 mark) Substituting the values from method (i): PMT = 4,594,573.09 * [0.08 * (1 + 0.08)^15] / [(1 + 0.08)^15 - 1] ≈ 298,841.38 Substituting the values from method (ii): PV = 298,841.38 * [(1 - (1 + 0.08)^(-15)) / 0.08] ≈ 4,594,573.09 Therefore, the present values of the two repayment methods are the same, demonstrating their equivalence. Both methods result in the same total amount of money being paid over the 5-year period.