Question

Part A: supernormal-growth stock valuation

A firm’s cash dividend is expected to grow at the following rates for the next 5 years. From year 6 on, its growth rate stabilizes at 5% into the foreseeable future. The firm’s required rate of return is 11.75%, and its most-recent dividend was at $1.75 per share.

Year	1	2	3	4	5	6 to infinity
Growth rate per year, %	30	25	20	15	10	5

i. Estimate the firm’s current stock price in $wx.yz format

ii. If the stock is trading at $50.00 per share, what is the implied required rate of return? Give answer in % to 4 decimal places. [Hint: use Data, What-if analysis, and Goal seek functions.]

May use IRR

Answer 1

i.

Year	Cash Flow					Discounting Factor [1/(1.1175^year)]	PV of Cash Flow (cash flow*discounting factor)
1	1.75	+	30%	=	2.275	0.894854586	2.035794183
2	2.275	+	25%	=	2.84375	0.80076473	2.277174702
3	2.8438	+	20%	=	3.4125	0.716567991	2.44528827
4	3.4125	+	15%	=	3.924375	0.641224153	2.516404037
5	3.9244	+	10%	=	4.316813	0.573802374	2.476997262
5	Terminal Value= (4.3168+5%)/ (11.75%-5%)				67.15022	0.573802374	38.53095695
					Expected Share Price today =sum of PVs		50.2826154

Current Stock Price = $50.28

ii.

		10%		11%		12.00%
Period	Cash Flow	Discountig Factor [1/(1.1^period)]	PV of cash flows (cash flow*discounting factor)	Discountig Factor [1/(1.11^period)]	PV of cash flows (cash flow*discounting factor)	Discountig Factor [1/(1.12^period)]	PV of cash flows (cash flow*discounting factor)
0	-50	1	-50	1	-50	1	-50
1	2.275	0.9090909	2.06818182	0.9009009	2.04954955	0.8928571	2.03125
2	2.84375	0.8264463	2.35020661	0.8116224	2.308051295	0.7971939	2.2670201
3	3.4125	0.7513148	2.56386176	0.7311914	2.495190589	0.7117802	2.4289501
4	3.924375	0.6830135	2.68040093	0.658731	2.585107367	0.6355181	2.4940113
5	4.316813	0.6209213	2.68040124	0.5934513	2.561818408	0.5674269	2.4494756
5	67.15022	0.6209213	41.6950034	0.5934513	39.85038724	0.5674269	38.102838
		PV =	4.0380558	PV =	1.850104446	PV =	-0.226455

IRR is the rate of return at which NPV=0

Here, NPV@11% is positive and @12% is negative.

Therefore, IRR is between 11% and 12%

IRR = Rate at which positive NPV + [Positive NPV/(Positive NPV-Negative NPV)]

= 11% + [1.8501/(1.8501-(-0.2265)]

= 11% + [1.8501/2.0766]

= 11% + 0.8909% = 11.8909%

(Explanation & Logic of the method: NPV @11% is 1.8501 and NPV@12% is -0.2265. i.e. 1% increase in required rate of return reduces NPV by 1.8501+0.2265 =2.0766. We want NPV=0. Therefore, Proportionate increase in required rate of return to reduce NPV by 1.8501 is calculated)