STAT3904_A1_Sol_1516_2nd

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3904

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Statistics

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Nov 24, 2024

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STAT3904 : Corporate Finance for Actuarial Science Assignment 1 - Solution 1. (a) Expected cash inflows of project B = 1 3 (4+6+8) = 6, and C = 1 3 (5+5 . 5+6) = 5 . 5. (b) Expected returns of stock X = 1 3 (80 + 110 + 140) / 95 . 65 - 1 = 15%, Y = 1 3 (40 + 44 + 48) / 40 - 1 = 10%, and Z = 1 3 (8 + 12 + 16) / 10 - 1 = 20%. (c) By checking the percentage differences slump vs normal, and boom vs normal for B, C, X, Y, Z , we can match up project B with stock Z , and project C with stock Y which have the same level of risk. Therefore, using (b), the opportunity costs for B = 20% and for C = 10%. (d) The NPVs: B = 6 / 1 . 2 - 5 = 0 and of C = 5 . 5 / 1 . 1 - 5 = 0. (e) The total market value of company’s shares remains unchanged since the NPVs of both projects are zeros. 2. Let the level payment be P which can be obtained as: 20000 = Pa 12 | 8% = P ( 1 - (1 . 08) - 12 0 . 08 ) which is 2653.9. 3. Using the relationship between the spot rates and the forward rates (1 + r n ) n = Q n i =1 (1 + f i ) for n = 1 , 2 , 3 , . . . , results in r 2 = 6 . 1998% , r 3 = 6 . 4990% , r 4 = 6 . 6987% , r 5 = 6 . 9973% . Note that r n increases as n increases, and thus we may conclude that the expected future interest rates increase. 4. As the real interest rate for one year is (1 . 1) / (1 . 04), the real value of this investment at the end of a year is $1057.69. 5. We can find the following table: Year PV(9%) % of total PV % × Year 1 137614.679 0.235864639 0.235864639 2 126251.999 0.216389577 0.432779154 3 115827.522 0.198522548 0.595567644 4 106263.782 0.182130778 0.718523112 5 97489.7079 0.167092457 0.835462284 Total 583447.6895 2.828196836 1

Therefore, given the duration D = 2 . 8282, and using the approximation method ( Δ V Δ j = - DV 1+ j ), it follows that Δ V = - 2 . 8282(583447 . 6895) 1 + 0 . 09 × 0 . 005 = - 7569 . 2886 . 6. The dividends form an increasing annuity immediate and an increasing perpetuity immediate starting at 3. Thus the current value follows 1 . 2 1 . 15 + 1 . 2 2 1 . 15 2 + 1 . 2 3 1 . 15 3 + 1 . 2 3 × 1 . 05 0 . 15 - 0 . 05 1 1 . 15 3 = 15 . 198 7. For the market capitalization rate 10%, V A = 10 0 . 1 = 100 , V B = 5 0 . 1 - 0 . 04 = 83 . 333 , and V C = 6 X t =1 5 1 . 2 t - 1 1 . 1 t ! + 1 1 . 1 6 × 5(1 . 2) 5 0 . 1 = 104 . 5051 . Hence, the stock C is the most valuable. For the market capitalization rate 7%, V A = 142 . 8571 , V B = 166 . 6667 , V C = 156 . 4987 , and thus the stock B is the most valuable in this case. 8. (a) A higher IRR does NOT mean the project has a higher NPV since it ignores the scale of the project. (b) The incremental IRR can be founded as: Project C 0 C 1 C 2 IRR(%) A-B -200 110 121 10% Since the incremental IRR is higher than the opportunity cost of capital 9%, the extra money put is profitable, i.e. the project A should be undertaken. (c) The NPVs of both projects can be calculated as NPV A = - 400 + 250 1 . 09 + 300 1 . 09 2 = 81 . 8618 , NPV B = 79 . 1011 . In other words, the NPV of the project A is higher than the NPV of the project B. 2

9. The PIs for the projects 1-7 are given Project 1 2 3 4 5 6 7 PI 0.22 -0.02 0.17 0.14 0.07 0.18 0.12 Then the projects 1,3,4,6 should be selected since its WAPI is the highest. 10. A growing perpetuity with a negative growth rate of -0.02 is PV = 1000 0 . 05 - ( - 0 . 02) = $14 , 285 . 71 . 11. (a) To compute the IRR, set the NPV=0 and solve for r , NPV = 50 , 000 - 4 , 400 r 1 - 1 (1 + r ) 12 ! . Using the spreadsheet gives the monthly IRR is 0.8484%, so the EAR is 10.67% ((1 . 1008484) 12 = 1 . 106696). Professor Chan’s cost of capital is 15%, so based on the IRR rule, she should turn down this opportunity. (b) When the EAR is 15%, after one month you will have (1 . 15) 1 / 12 = 1 . 011715 , so the monthly discount rate is 1.1715%. Computing the NPV using this discount rate yields NPV = 50 , 000 - 4 , 400 0 . 011715 1 - 1 (1 + 0 . 011715) 12 ! = $1 , 010 . 06 . Therefore, the correct decision is to accept the deal. 3

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