12-13 Skyline Corp. will invest $130,000 in a project that will not begin to produce returns until after the 3rd year. From the end of the 3rd year until the end of the 12th year(10 periods), the annual cash flow will be $34,000. If the cost of capital is 12 percent, should this project be undertaken? Solution: Skyline Corporation Present value of inflows Find the present value of a deferred annuity A $34,000n=10,i=12% PVA =AX PVIFA (Appendix D) PVA=$34000X5650=$192,100 Discount from Beginning of the third period(end of second period to resent FV=$192,100,n=2,i=12% PⅤ=FVxPⅤF( Appendix b) PV$192,100x.797=$153,104 Present value of inflows $153,104 Present value of outflows 130000 Net present value $23,104 The net present value is positive and the project should be undertaken CopyrightC 2005 by The McGray-Hill Companies, Inc. S-436
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-436 12-13. Skyline Corp. will invest $130,000 in a project that will not begin to produce returns until after the 3rd year. From the end of the 3rd year until the end of the 12th year (10 periods), the annual cash flow will be $34,000. If the cost of capital is 12 percent, should this project be undertaken? Solution: Skyline Corporation Present Value of Inflows Find the Present Value of a Deferred Annuity A = $34,000, n = 10, i = 12% PVA = A x PVIFA (Appendix D) PVA = $34,000 x 5.650 = $192,100 Discount from Beginning of the third period (end of second period to present): FV = $192,100, n = 2, i = 12% PV = FV x PVIF (Appendix B) PV = $192,100 x .797 = $153,104 Present value of inflows $153,104 Present value of outflows 130,000 Net present value $ 23,104 The net present value is positive and the project should be undertaken
12-14. The Ogden Corporation makes an investment of $25,000, which yields the following cash flows. Year Cash Flow 2345 8.000 9.000 10000 a. What is the present value with a 9 percent discount rate(cost of capital)? b. What is the internal rate of return? Use the interpolation procedure shown in this chapter c. In this problem would you make the same decision under both parts a and Solution: Ogden Corporation Year Cash Flow x PVIF 9%= Present Value 1$5000 917 $4,585 5.000 842 4.210 8.000 772 6.176 4 9,000 708 6,372 10.000 650 6500 Present value of inflows $27,843 Present value of outflows 25.000 Net present value $2,843 b. Since we have a positive net present value the internal rate of return must be larger than 9%. Because of uneven cash flows, we need to use trial and error. Counting the net present value calculation as the first trial we now try 11% for our second trial S-437 Copyright C2005 by The McGra-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-437 12-14. The Ogden Corporation makes an investment of $25,000, which yields the following cash flows: Year Cash Flow 1 ....................................... $ 5,000 2 ....................................... 5,000 3 ....................................... 8,000 4 ....................................... 9,000 5 ....................................... 10,000 a. What is the present value with a 9 percent discount rate (cost of capital)? b. What is the internal rate of return? Use the interpolation procedure shown in this chapter. c. In this problem would you make the same decision under both parts a and b? Solution: Ogden Corporation a. Year Cash Flow x PVIF @ 9% = Present Value 1 $ 5,000 .917 $ 4,585 2 5,000 .842 4,210 3 8,000 .772 6,176 4 9,000 .708 6,372 5 10,000 .650 6,500 Present value of inflows $27,843 Present value of outflows –25,000 Net present value $ 2,843 b. Since we have a positive net present value, the internal rate of return must be larger than 9%. Because of uneven cash flows, we need to use trial and error. Counting the net present value calculation as the first trial, we now try 11% for our second trial
12-14. Continued Year Cash Flow x PVIF 11%= Present Value $5000 901 $4,505 5.000 812 4.060 2345 8.000 5848 9.000 659 5931 10.000 5930 Present value of inflows $26,274 a two percent increase in the discount rate has eliminated over one half of the net present value so another two percent should be close to e answer Year Cash FlOw X PVIea 13% Present value $5000 885 $4425 5,0 783 3.915 2345 8.000 6 5.544 9.000 613 5517 10.000 543 5430 Present value of inflows 524831 $26,274 PⅤ@11%$26,274 PⅤa11% 24.831 PV@13%25000 Cost $1443 $1,274 11%+ $1,274 S143Q%=11%+.883(2%)=11%+1.7%=12.77 pproximately the same answer can be derived by interpolating between 12% and 13% instead of 11% and 13% c. Yes, both the NPv is greater than 0 and the irr is greater than the cost of capital CopyrightC 2005 by The McGray-Hill Companies, Inc. S-438
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-438 12-14. Continued Year Cash Flow x PVIF @ 11% = Present Value 1 $ 5,000 .901 $ 4,505 2 5,000 .812 4,060 3 8,000 .731 5,848 4 9,000 .659 5,931 5 10,000 .593 5,930 Present value of inflows $26,274 A two percent increase in the discount rate has eliminated over onehalf of the net present value so another two percent should be close to the answer. Year Cash Flow x PVIF @ 13% = Present Value 1 $ 5,000 .885 $ 4,425 2 5,000 .783 3,915 3 8,000 .693 5,544 4 9,000 .613 5,517 5 10,000 .543 5,430 Present value of inflows $24,831 $26,274...............PV @ 11% 24,831...............PV @ 13% $ 1,443 $26,274 ...............PV @ 11% 25,000...............Cost $ 1,274 11% + $1,443 $1,274 (2%) = 11% + .883 (2%) = 11% + 1.77% = 12.77% Approximately the same answer can be derived by interpolating between 12% and 13% instead of 11% and 13%. c. Yes, both the NPV is greater than 0 and the IRR is greater than the cost of capital
12-15 The Danforth Tire Company is considering the purchase of a new machine that would increase the speed of manufacturing and save money The net cost of this machine is $66,000. The annual cash flows have the following projections Year Cash flow 29.000 36.00 16,000 a. If the cost of capital is 10 percent, what is the net present value? b. What is the internal rate of return? c. Should the project be accepted? Why? Solution: The Danforth Tire Company a. Net Present value Year Cash Flow 10%PV1 Present value $21000 909 $19,089 29.000 826 23.954 3 36.000 27.036 16.000 683 10,928 8.000 621 4968 Present value of inflows 85.975 Present value of outflows 6000 Net present value $19,975 S-439 Copyright C2005 by The McGra-Hill Companies, Inc
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-439 12-15. The Danforth Tire Company is considering the purchase of a new machine that would increase the speed of manufacturing and save money. The net cost of this machine is $66,000. The annual cash flows have the following projections. Year Cash Flow 1 ....................................... $21,000 2 ....................................... 29,000 3 ....................................... 36,000 4 ....................................... 16,000 5 ....................................... 8,000 a. If the cost of capital is 10 percent, what is the net present value? b. What is the internal rate of return? c. Should the project be accepted? Why? Solution: The Danforth Tire Company a. Net Present Value Year Cash Flow x 10% PVIF Present Value 1 $21,000 .909 $19,089 2 29,000 .826 23,954 3 36,000 .751 27,036 4 16,000 .683 10,928 5 8,000 .621 4,968 Present value of inflows $85,975 Present value of outflows –66,000 Net present value $19,975
12-15. Continued b. Internal rate of return We will average the inflows to arrive at an assumed annuity $21.000 29.000 36.000 16.000 8.000 $110000/5=$22,000 We divide the investment by the assumed annuity value $66000 $22000 =3PV Using Appendix d for n=5, 20% appears to be a reasonable first approximation(2.991). We try 20% YEar Cash flow x20%PⅤI Present value $21000 833 $17493 29.000 694 20,126 2345 36000 579 20.844 16.000 482 7,712 8,000 402 Present value of inflows $69.391 Since 20% is not high enough, we try the next highest rate at 25%0 CopyrightC 2005 by The McGray-Hill Companies, Inc. S-440
Copyright © 2005 by The McGraw-Hill Companies, Inc. S-440 12-15. Continued b. Internal Rate of Return We will average the inflows to arrive at an assumed annuity. $ 21,000 29,000 36,000 16,000 8,000 $110,000/5 = $22,000 We divide the investment by the assumed annuity value. 3 PVIFA $22,000 $66,000 = Using Appendix D for n = 5, 20% appears to be a reasonable first approximation (2.991). We try 20%. Year Cash Flow x 20% PVIF = Present Value 1 $21,000 .833 $17,493 2 29,000 .694 20,126 3 36,000 .579 20,844 4 16,000 .482 7,712 5 8,000 .402 3,216 Present value of inflows $69,391 Since 20% is not high enough, we try the next highest rate at 25%