password to the pdf:advfin20

1.
(a) Given:
    u
    1.2
    
    d
    0.9
    
    time
    10
    Years
    Rate
    10%
    
    Spot Price
    10
    Million
    Expected lower Future Spot price(P1)
    9
    Million
    Expected Upper Future Spot price(P2)
    12
    Million
Formula for calculating the probability of higher price is:
[(ert – 0.90) / (1.20 – 0.90)]
= [(1.11 – 0.90) / (0.30)]
= 70%
Formula for calculating the probability of lower price is:
= [(1.20 - ert) / (1.20 – 0.90)]
= [(1.20 – 1.11) / (0.30)]
= 30%
As per the calculations made in the excel file, we can see that the value of option has started decreasing at the end of year 5. Hence, we should cut the trees at 5th year and not till the trees are growing.
(b) It is optimal to cut in the 1st year because after that the value of investment has started decreasing due to rent.
The value of Investment =$9.56 million
(Note: The calculations are made in the Excel file).
2. Given:
Current Gold Price = $1500
u = 1.20
Value at upper limit (Cu)= 1500 x 1.20
= $1800
D = 0.90
Value at lower limit (Cd)= 1500 x 0.90
= $1350
Time (t) = 3 years
Rate (r) = 2%
Formula for calculating the value of an Option:
Cu x [(ert – 0.90) / (1.20 – 0.90)] + Cd x [(1.20 - ert) / (1.20 – 0.90)]
= 1800 x [(1.06 – 0.90) / (0.30)] + 1350 x [(1.20 – 1.06) / (0.30)]
= 960 + 630
= $1590
(a) The value of this investment Opportunity is:
PV of Gold Value – PV of Fixed cost – PV of Variable cost – Initial Investment cost
= (1590 x 10000 x 3) – (10000000 / 1.06) – [(500 x 10000 x 3) / 1.06] – 1,500,000
= 47,700,000 – 9,433,962 – 14,150,943 – 1,500,000
= $22,615,095
Hence the value of this Investment Opportunity is $22,615,095.
(Note: The calculations are made in the Excel file)
3.
(a) Given:
Dividend Yield Rate = n
Current Stock Price = So
Stock Price Volatility =
Total Return from Stock = r
Growth rate = r - n
The expected stock price using Gordon’s Growth Model is:
= So x (1 + r - n) / r – r +n
= So x (1 + r - n) / n
Hence the expected stock price at maturity T is So x (1 + r - n) / n.
(b) The expected pay-off from the call option is:
Variable...