Question

"You are investing $6,000 immediately in a stock that you will keep for 13 years. At the end of 13 years, the stock will be worth $16,813 with a probability of 0.48 and worth $22,785 with a probability of 0.52. When you sell the stock, you will need to pay taxes on the profit earned from selling the stock (i.e., taxes on the difference between the selling and buying prices of the stock). The tax rate will be 8% with a probability of 0.8 or 16% with a probability of 0.2. Your MARR is 4.7% What is the variance of the net present worth from investing in the stock?"

Answer 1

(a)	(b)	(c = b - a)	(T1)	(T2)	d = (c*T1*P1)+(C*T2*P2)	(e = d - a)	f = e/(1+4.7%)^13	(f - a)
Initial investment	Amount after 13 years	Profit	Tax with prob. P1 = 0.8	Tax with prob. P2 = 0.2	Tax	Net profit	PV of Net profit	NPW
6,000	16,813	10,813	8%	16%	1,038.05	9,774.95	5,380.32	(619.68)
6,000	22,785	16,785	8%	16%	1,611.36	15,173.64	8,351.85	2,351.85

(p)	(a)	(b)
Probability	NPW	Weighted NPW	p*(a-m)^2
48%	(619.68)	(297.45)	1,146,068.72
52%	2,351.85	1,222.96	1,057,909.59
	(m)	925.52	2,203,978.31

Variance of Net Present Worth (NPW) = 2,203,978.31