Question

Capital Budgeting is the financial planning component of business. Companies analyze various business alternatives to discover which alternatives are profitable. In order to invest in various projects corporations need to raise capital from many sources including stocks, preferred stocks, bonds, and retained earnings (undistributed profits). Each of these sources of funds have a cost associated with them. Stock holders expect and return, bond holders expect interest payments, and stock holders expect the company to utilize internal resources in the most profitable manner for long term operations. The debt structures of different companies result in different costs of capital for each firm. The weighted cost of capital is the weighted average cost of all the forms of financing and company currently employees and the marginal cost of capital is the cost for the next dollars of financing available to the firm. The computation of these items is left for a course in finance and accounting. For our purposes we will assume that these costs will be given as a required rate or return for the firm for given projects under consideration. The basic assumption of capital budgeting is that cash flows occurring at different intervals must be reconciled to one time frame for the comparison of appropriate profitability. Generally the time frame of preference is the present. The present value of all future cash flows is compare to the present value of all costs for the project to determine its net present value, NPV. If the net present value is positive then the firm should undertake the project in question. If two mutually exclusive projects are under consideration the one with the greatest NPV would be chosen. To determine the actual return to be achieved by the firm for a given capital project the internal rate of return must be computed. The internal rate of return, IRR, is the rate that mathematically results in an net present value of zero. This is generally a iterative computation preformed in a similar manner to that of the computation of bond yields. Generally, a project with a IRR greater than that of the cost of capital or required rate of return is accepted and on with a lower rate of return than the cost of capital is rejected. Often it is useful to plot various NPV's for a given project as a function of various required rates of return. This curvilinear graph is referred to as the net present value profile. For multiple projects that are mutually exclusive these charts are useful for comparison.

Problems 1. For the following cash flows for the following three investment options, calculate the NPV net present value.

2. For the following cash flows for the following three investment options calculate IRR internal rate of return.

3. For the following cash flows for the following three investment options calculate the payback period.

4. Which projects would be accepted and which ones would be rejected, if we assume a cost of capital of 10%?

Investment Options

Year a    b c

0 ($100,000) ($100,000) ($100,000)

1    $55,000 $15,000 $90,000

2    $50,000 $20,000 $30,000

3    $30,000 $25,000 $7,500

4 0 $50,000    0

5 0    $50,000 0

Answer 1

		A	B	C
1	NPV	79058.50	-51051.84	12246.43
2	IRR	38.78%	-20.41%	20.16%
3	Payback	1.90	Never	1.33

4: Accept A and C since their IRR is more than the cost of capital.

Workings

Payback = Year in which Cumulative CF is last negative -(Last negative cumulative CF/ CF of next year

Year	A	Cumulative CF	B	Cumulative CF	C	Cumulative CF
0	-100000	-100000	-100000	-100000	-100000	-100000
1	55000	-45000	15000	-85000	90000	-10000
2	50000	5000	20000	-65000	30000	20000
3	30000	35000	25000	-40000	7500	27500
4	50000	85000	0	-40000	0	27500
5	50000	135000	0	-40000	0	27500

Sign in AutoSave Off Вook1 - Excel X O Tell me what you want to do Share File Formulas Review View Help Comments Home Insert Draw Page Layout Data KEInsert X 10 ab A A Calibri General xDelete- Paste Cell Conditional Format as Sort & Find & BIU -A E - $% Format 00 T T T T Formatting Table Styles Filter Select Clipboard Alignment Cells Editing Font г. Number Г. Styles A Year В1 A В C D E G K A Cumulative CF Cumulative CF C Cumulative CF 1 Year -100000 -100000 G2 2. 0 =C2 -100000 E2 55000 -D2+C3 15000 F2+E3 90000 H2+G3 ЕН3+G4 2 50000 -D3+C4 20000 -F3+E4 30000 5 D4+C5 F4+E5 =H4+G5 30000 25000 7500 =D5 +C6 =F5 + E6 6 H5+G6 50000 0 0 7 D6+C7 =F6+E7 H6+G7 5 50000 0 0 8 9 A В C NPV(10%,C3:C7)+C2 =NPV(10 % , E3:E7)+E2 =NPV(10 %,G3:G7)+G2 IRR(C2:C7) 10 1 NPV 11 2 =IRR(E2:E7) IRR(G2:G7) IRR 12 3 Payback B3-D3/C4 B3-H3/G4 Never 13 14 15 16 17