An all equity firm pays a dividend of $1 in first year, a dividend of $2...

An all equity firm pays a dividend of $1 in first year, a dividend

of $2 in second year which then grows at a constant rate of 5% for the next ten years. After that, the company has promised to pay a fixed dividend of $4 annually. If the cost of equity is 15%, what is the share price?

Select one:
a. $20.33
b. $22.60
c. $23.25
d. $21.5

Expert Solution

Year	0	1	2	3	4	5	6	7	8	9	10	11	12
Dividend CFs(Prev. *1.05 from yrs. 3 to 12)		1	2	2.1	2.205	2.31525	2.43101	2.55256	2.68019	2.8142	2.95491	3.102656	3.257789
Terminal divs.(4/15%)													26.66667
Total		1	2	2.1	2.205	2.31525	2.43101	2.55256	2.68019	2.8142	2.95491	3.102656	29.92446
PV F at 15%(1/1.15^yr.n)		0.86957	0.75614	0.65752	0.57175	0.49718	0.43233	0.37594	0.32690	0.28426	0.24718	0.21494	0.18691
PV at 15%(Total*PVF)		0.86957	1.51229	1.38078	1.26072	1.15109	1.05099	0.95960	0.87616	0.79997	0.73041	0.66689	5.59309
Share price (sum of PVs)	16.85157
ie.	16.85

Share price is the present values of all future expected dividend cash flows,discounted at the cost of equity

ie. PV of Yr.1 div.+PV of Yr. 2 div.+PV of growing annuity for next 10 yrs.(ie. Yr.3 to 12)+PV of the PV of perpetuity at end yr.12

ie.(1/1.15^1)+(2/1.15^2)+((2.1/(15%-5%)*(1+(1.05/1.15)^9))/1.15^2)+((4/15%)/1.15^12)=

16.85157

16.85

Hence the answer is $ 16.85

None of the given answers are correct

jeff jeffy answered 2 years ago

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