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# Simple Finance Problems for Present and Future Values

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Estimate the present and future values of the following income streams. The annual interest rate is 12% compounded monthly.

The A Venture Capital is expected to grow at annual rate of 18% for the next four years, then at 12% for another three years, and finally settle down to a growth rate of 6% for the indefinite future. Its common stock currently pays a \$0.60 dividend, but dividends are expected to increased in proportion ot the growth of the HVC. Given the AVC's cost of capital 12%, (a) estimate the current market value of AVC's common stock; and (b) what would be the price per share at the end of 5 years?

Estimate (i) stock price per share as of today; (ii) beta; (iii) required rate of return; and (iv) internal rate of return. Additionally, please draw the security market line to show the under- or over-priced situation of XYZ's common stock.

The dividend is expected to grow at an annual rate of 15% for the next 10 years, then grow indefinitely at a slower growth rate of 12% per year. (i) Estimate the market price of common stock as of today; and (ii) what would be the price per share if you sell common stock at the end of 5 years.

i. Rank the three projects based on the risk-adjusted IRR method
ii. Rank the three projects based on the risk-adjusted NPV method
iii. Which project would you prefer?

#### Solution Preview

1. Estimate the present and future values of the following income streams. The annual interest rate is 12% compounded monthly.

Year

0 1 2 3 ....... 99 100

\$5 \$10 \$5 \$10 \$5 \$10 ........ \$10 \$5 \$10

we can calculate the two payments separately:
\$5 is paid semiannually, and another \$5 is paid yearly.
Using a TI BaII plus calculator, just insert: (if you don't have this kind of calculator, you can easily use the functions in MS EXCEL)
For the semiannual \$5: N=100*2=200, I/Y (interest rate) = 12/2=6, PMT=5, FV=0
The CPT -> PV= 83.33
For the annual \$5: N=100, I/Y (interest rate) = 12, PMT=5, FV=0
The CPT -> PV= 41.67
Then the total PV=83.33+41.67=125

For future value: N=100, I/Y= 12, PMT=0, PV=125
The CPT -> FV= 10,440,283.22
Yes, it is very surprising!

2. The A Venture Capital is expected to grow at annual rate of 18% for the next four years, then at 12% for another three years, and finally settle down to a growth rate of 6% for the indefinite future. Its common stock currently pays a \$0.60 dividend, but dividends are expected to increased in proportion at the growth of the HVC. Given the AVC's cost of capital 12%, (a) estimate the current market value of AVC's common stock; and (b) what would be the price per share at the end of 5 years?

a)The dividends, from this year to 7 years will be
Year Growth Dividend PV
0 0.6 0.6
1 18% 0.708 0.632
2 18% 0.835 0.666
3 18% 0.986 0.702
4 18% 1.163 0.739
5 12% 1.303 0.739
6 12% 1.459 0.739
7 12% 1.634 0.739
8 6% 1.732
* discounted at cost of capital 12%
At the end of year 7, the price of the stock can be calculated by formula:
P7=D8 / (r-g) =1.732/(0.12-0.08) =43.3
Then the PV of P7 is PV7=P7/(1+r)^7= 19.587
Adding up all the PVs, you can get P0 = \$24.543

(b) what would be the price per share at the end of 5 years?
This is jus the FV5 of P0, i.e. P5= P0*(1+r)^5=25.144*(1+0.12)^5=\$44.31

3. You have collected the following data for ABC Company: (i) Estimate the total risk, systematic risk, and unsystematic risk of ABC's common stock.

State Probability Rabc Rm
...

#### Solution Summary

The present and future values of functions are analyzed. The income streams are estimated and monthly compounds are estimated.

\$2.49