Question

The annual data on stock prices and dividends for Microsoft Corporation(MSFT) is as follows:

Year Price (Beginning of the Year) Price (End of the Year) Dividends (End of the Year )

2005 26.28 28.15 0.29

2006 28.15 30.86 0.33

2007 30.86 32.60 0.37

2008 32.60 17.10 0.41

2009 17.10 28.18 0.46

2010 28.18 27.73 0.55

2011 27.73 29.53 0.68

2012 29.53 27.45 0.83

2013 27.45 37.84 0.97

2014 37.84 46.45 1.15

What will be the IRR if the stock is bought at the beginning of 2010 and sold at the end of 2014?

19.14%

9.72%

13.24%

12.87%

Answer 1

Purchase value of the stock at the beginning of 2010	28.18
Sale value of the stock at the end of 2014	46.45

NPV @ 10%

Details	2010	2011	2012	2013	2014
Year	1	2	3	4	5
Dividend for the year	0.55	0.68	0.83	0.97	1.15
Sale value of the stock at the end of 2014					46.45
Total cashflows	0.55	0.68	0.83	0.97	47.60
PV factor @ 10%	0.89	0.83	0.75	0.68	0.62
PV cashflows (Total cashflows x PV factor)	0.49	0.56	0.62	0.66	29.56
Total PV of cashflows	31.89
Purchase value of the stock at the beginning of 2010	28.18
NPV (Total PV of cashflows - Purchase value of stock)	3.71

NPV @ 13%

Details	2010	2011	2012	2013	2014
Year	1	2	3	4	5
Dividend for the year	0.55	0.68	0.83	0.97	1.15
Sale value of the stock at the end of 2014					46.45
Total cashflows	0.55	0.68	0.83	0.97	47.60
PV factor @ 13%	0.88	0.78	0.69	0.61	0.54
PV cashflows (Total cashflows x PV factor)	0.49	0.53	0.58	0.59	25.84
Total PV of cashflows	28.02
Purchase value of the stock at the beginning of 2010	28.18
NPV (Total PV of cashflows - Purchase value of stock)	(0.16)

IRR computation

NPV at lower discount rate	3.71
Lower discount rate	10.00%
Value at higher discount rate	(0.16)
Higher discount rate	13.00%
Step 1 : Higher discount rate - Lower discount rate	3.00%
Step2 : NPV at lower discount rate x step1	0.11
Step3 : NPV at lower discount rate - NPV at higher discount rate	3.87
Step4 : Step2 / Step 3	2.88%
Step 5 : Lower discount rate + step4 ---IRR	12.88%

Therefore the answer is Option4 ---> 12.87%. As we have used interpolation method approximate answer can be computed using above method. However, more accurate IRR computation can be done using excel IRR function.

Hope this helps you answer the question. Please leave your feedback or rating on the same.

Thanks