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?
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Solution Summary
The present and future values of functions are analyzed. The income streams are estimated and monthly compounds are estimated.
Solution Preview
please refer to the attachment.
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
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