Question

1

A. What is the net present value (NPV) of an investment of $1000 that returns $1500 in three years, using a discount rate of 10%?

B. What is the NPV of a $5000 investment that is worth $10,000 at the end of five years, if we wanted to earn 15% on the investment?Did we earn our required 15%?  How can you tell?

C. What is the present value of a stock that pays a $1 dividend in perpetuity, if you wish to earn a 10% return?  What would you be willing to pay for the stock?

D. . You are considering buying stock in a company that currently pays a $1 annual dividend.  The dividend is expected to increase by 3% annually in perpetuity, and you wish to earn a 12% return on the investment.  How much would you be willing to pay for the stock?

E. You are considering an investment in an existing company; the company pays a $3.00 quarterly dividend per share.  After three years you believe that you can sell the stock for $100 per share.  If you wish to earn a 12% return, how much would you be willing to pay for the stock today?  (hint:  this is a quarterly dividend, so the discounting period is a quarter, and the quarterly discount rate is the annual rate divided by 4.  Set this up in an Excel file for the calculations).

Answer 1

Question A:

NPV of the investment = Present Value of Cahs Inflows - Initial investment

= [$1,500 / (1+10%)^3] - $1,000

= [$1,500 / 1.331] - $1,000

= $1,126.9722 - $1,000

= $126.97

Therefore, NPV of the investment is $126.97

Question B:

NPV of the investment = Present Value of Cahs Inflows - Initial investment

= [$10,000 / (1+15%)^5] - $5,000

= [$10,000 / 2.01135719] - $5,000

= $4,971.76735 - $5,000

= -$28.23265

NPV of the investment is -$28.23

We didn't earn 15% return since NPV < 0

Question C:

Dividend = $1

r = required return = 10%

Current stock price = Dividend / Required return

= $1 / 10%

= $10

Therefore, the amount willing to pay for stock is $10

Question D:

D0 = Current dividend = $1

g = growth rate = 3%

r = required return = 12%

D1 = Expected Dividend = D0 * (1+g) = $1 * (1+3%) = $1.03

Current price of Stock = D1 / (r - g)

= $1.03 / (12%-3%)

= $11.44444444

Therefore, the most willing to pay for the stock is $11.44

Question E:

Calculation of Present Value of Future Dividends
Quarter	Cash Flows	Discount Factor @3%	Discounted Cash Flows
A	B	C = 1/(1+3%)^A	D = B*C
1	3	0.970873786	2.912621359
2	3	0.942595909	2.827787727
3	3	0.915141659	2.745424978
4	3	0.888487048	2.665461144
5	3	0.862608784	2.587826353
6	3	0.837484257	2.51245277
7	3	0.813091511	2.439274534
8	3	0.789409234	2.368227703
9	3	0.766416732	2.299250197
10	3	0.744093915	2.232281745
11	3	0.722421277	2.16726383
12	103	0.70137988	72.24212766
Present Value	100.00
Therefore, the most willing to pay for stock is $100