Numerical of Capital Budgeting

Questions:

1) What is Capital Budgeting? How it is helpful for taking long term decisions?

2) What are the tools used in capital budgeting?

3) How NPV helps to take an investment decision? Explain.

4) How IRR is better than NPV and if not? Explain the reason.

5) Suppose Mr. Sharma has decided to invest his Rs.2, 00,000 of saving in share market. But he gets confused in which companies he should invest to get enough return after 5 years:

· Company A: Rate of return 8% annually, expected cash flow – Rs. 1, 80,000 per year

· Company C: Rate of return 7% quarterly, expected cash flow – Rs. 3, 80,000 per year

· Company P: Rate of return 7.9% semi-annually, expected cash flow – Rs. 2, 10,000 per year

Find out which investment is best for Mr. Sharma with the help of Payback period.

Solution: Company A:

Payback period = Initial investment/Annual cash flow

= 2, 00,000 / 180,000 = 1.11 years

Company B:

Payback period = Initial investment/Annual cash flow

= 2, 00,000 / 380,000 = 0.52 years

Company C:

Payback period = Initial investment/Annual cash flow

= 2, 00,000 / 2, 10,000 = 0.95 years

Company B is best option for Mr. Sharma.

6) Find out the IRR in below investment with the help of following information:

Company	Expected cash flow	Rate of return	Time period	Initial amount invested
ABC	1^st -45, 000, 2^nd-52, 000, 3^rd-38, 000, 4^th-24, 000	7.2 % semi-annually	4 year	1, 00,000
PQR	2, 50,000	8% quarterly	4 year	2, 40,000
XYZ	3,40, 000	8.6% semi-annually	4 year	4, 00,000

Solution: IRR is a rate where NPV is zero.

ABC :Cash flow	Discount rate @7.2/2 = 3.6	Present value
45000	1.07 (1.036^2)	42,056.07
52000	1.15 (1.036^4)	45,217.39
38000	1.24 (1.036^6)	30,645.16
24000	1.33 (1.036^8)	18,045.11
Total		1,35,963.73
NPV	1,35,963.73- 1,00,000	35,963.73

The given discount rate is not an IRR because NPV is not equal to zero.

Let’s assume 23%

Cash flow	Discount rate @23/2 = 11.2	Present value
45000	1.243	36,202.735
52000	1.546	33,635.188
38000	1.921	19,781.364
24000	2.389	10,046.044
Total		99,665.331
NPV	99,665.331- 1,00,000	-334.669

IRR is 23% semi annually approximately

PQR: Let’s check 8% quarterly is IRR or not

= 2, 50,000/1.373 = 1, 80,083.03

Assume 24% quarterly

= 2, 50,000/2.5 = 1, 00,000

NPV = 1, 00,000 – 1, 00,000 = Rs. 0

So, IRR is 25 % quarterly

XYZ: Let’s check 8.6% semi annually is IRR or not

= 3, 40,000/1.4 = 2, 42,857.14

Assume 33% semi annually

= 3, 40,000/3.4 =1, 00,000

So, IRR is 33 % semi annually

7) Mr. Mehta invested his Rs. 1, 00,000 in following companies share for 5 years:

· Company Y gives 6.3% return for 3 years and after it gives 7.0% return.

· Company X gives 7.6% return for 2 year and after it provides 6.8% return.

· Company Z gives 6.5 % return for 5 years.

Particulars	Expected cash flows 1^st year	2^nd year	3^rd year	4^th year	5^th year
X	30, 000	40, 000	50, 000	20, 000	38, 000
Y	20, 000	25, 000	29, 000	35, 000	36, 000
Z	45, 000	48, 000	35, 000	39, 000	25,300

Mr. Mehta suffers a loss in his business and he needed Rs. 1, 00,000. Find out which investment matures first to fulfil his requirement.

Solution: Discounted payback period Company X:

Cash flow	Discounting factor	Present value	Cumulative Present value(-100,000)
30,000	1.063	28,222.013	-71,777.987
40,000	1.130	35,398.230	-36,379.757
50,000	1.201	41,631.973	5,252.216
20,000	1.311	15,255.530	20,507.746
38,000	1.403	27,084.818	47,592.564

X = 2 + (36,379.757/41,631.973)

= 2+0.87

= 2.87 years

Cash flow	Discounting factor	Present value	Cumulative Present value(-100,000)
20,000	1.076	18,587.361	-81,412.639
25,000	1.158	21,588.947	-59,823.692
29,000	1.218	23,809.524	-36,014.168
35,000	1.301	26,902.383	-9,111.785
36,000	1.389	25,917.927	16,806.142

Y = 4+ (9,111.785/25,917.927)

= 4+ 0.35

= 4.35 years

Cash flow	Discounting factor	Present value	Cumulative Present value(-100,000)
45,000	1.065	42,253.521	-57,746.479
48,000	1.134	42,328.042	-15,418.437
35,000	1.208	28,973.510	13,555.073
39,000	1.286	30,326.594	43,881.667
25,300	1.370	18,467.153	62,348.82

Z = 2+ (15,418.437/28,973.510)

= 2+0.53

= 2.53 years

Investment in Z Company is best option for Mr. Mehta.

8) The initial investment is Rs. 6, 00,000 and the profitability index is 78%. Find out the NPV for 5 year investment.

Solution: Net Profitability index = NPV/initial Investment

NPV = profitability index*initial investment

= 0.78*600000

= Rs. 4, 68,000

9) Find out the difference between:

· MIRR and IRR.

· Payback period and discounted payback period.

10) Find out the internal rate of return with the help of given information:

Particulars	Expected cash flows per year	NPV	Time period	Initial Investment
Company ABC	50, 000	60, 200	3 years	100,000
Company PQR	70, 000	40, 800	4 years	100,000

Solution:

ABC :Cash flow	Discount rate @23%	Present value
50000	1.23	40,650.407
50000	1.51	33,112.583
50000	1.86	26,881.720
Total		1,00,644.71
NPV	1,00,644.71- 1,00,000	644.71

PQR :Cash flow	Discount rate @ 48%	Present value
70000	1.48	47,297.298
70000	2.19	31,963.470
70000	3.24	21,604.938
Total		1,00,865.706
NPV	1,00,865.706- 1,00,000	865.706

11) Find out which investment gives higher return by using following investment evaluation techniques:

· Average rate of return

· Discounted payback period

· NPV

· Payback period

· IRR

Expected Cash inflows (in Rs.)

Rate of return

Initial investment

Time period

1^st year - 50,600;

2^nd year - 55, 000;

3^rdyear - 48, 000

5.8% annually

1, 00,000

3 years

1^st year – 55, 900

2^nd year – 22,330

3^rd year – 78, 250

4^th year – 48,000

5^th year – 62,000

5.2% semi- annually

2, 00,000

5 years

Solution:

Cash flow	Discount rate	Present value	Cumulative Cash flow (-1,00,000)	IRR @25% (assume)	Present value
50,600	1.058	47,826.087	-52,173.913	1.25	40,480
55,000	1.119	49,151.028	-3,022.885	1.56	35,256.41
48,000	1.184	40,540.541	37,517.656	1.95	24,615.385
1,53,600		1,37,571.656			1,00,351.795

NPV = 1, 37,571.656 – 1, 00,000 = Rs. 37,571.656

Average rate of return = 1, 53,600 /3= 51,200/1, 00,000 = 51.2%

Discounted payback period = 2+3022.885/40,540.541 = 2.07 years

Payback period = 1+ (49,400/55,000) = 1.90 years

IRR 25% approximate

Cash flow	Discount rate	Present value	Cumulative Cash flow (-2,00,000)	IRR @ 18% (assume half yearly)	Present value
55,900	1.026	54,483.431	-1,45,516.569	1.09	46,697.248
22,330	1.053	21,206.078	-1,24,310.491	1.188	18,796.297
78,250	1.080	72,453.704	-51,856.787	1.30	60,192.308
48,000	1.108	43,321.300	-8,535.487	1.412	33,994.334
62,000	1.137	54,529.464	45,993.977	1.539	40,285.90
2,66,480		2,48,993.977			1,99,966.087

NPV = Rs. (2, 48,993.977 -2, 00,000) = Rs. 48,993.977

IRR = 18% approximate

ARR = 2, 66,480/5 =53,296/2, 00,000 = 26.65%

Discounted payback period = 4+ 8,535.487/54,529.464 = 4.16 years

Payback period = 3+ (43,520/48,000) = 3.91 years

How to calculate Cost of Preference Share Capital?

Cost of Preference Share Capital: An amount paid by company as dividend to preference shareholder is known as Cost of Preference Share Capital. Preference share is a small unit of a company’s capital which bears fixed rate of dividend and holder of it gets dividend when company earn profit. Dividend payable is not a tax deductible amount. So, there is no tax adjustments required for comparing with cost of debt. Formula for Cost of Preference Share: Irredeemable Preference Share Redeemable Preference Share K p = Dp/NP K p = D p +((RV-NP)/n )/ (RV+NP)/2 Where, K p = Cost of Preference Share D p = Dividend on preference share NP = Net proceeds from issue of preference share (Issue price – Flotation cost) RV = Redemption Value N = Period of preference share Example: A company issues 20,000 irredeemable preference share at 8% whose face value is Rs.50 each at 4% discount. Find out the Cost of Preference Share Capital.

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Numerical of Capital Budgeting

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