Finance Answer Note #11

Question 1 answer this question: An investment has the potential of earning you $5000 at a 10 percent probability, $3000 at a 25 percent probability, and $2000 at a 65 percent probability, based on the performance of the stock market. The expected value of the investment is $? Answer The expected value of this investment can be calculated by multiplying the probability of each outcome by its corresponding monetary value, and then adding these values together. Therefore, the expected value is calculated as follows: Expected value = (0.10 x $5000) + (0.25 x $3000) + (0.65 x $2000) = $500 + $750 + $1300 = $2550 Therefore, the expected value of this investment is $2550. Question 2 A risk neutral investor in an uncertain environment is facing the following payoffs and probabilities for an investment project: Stronger dollar event: Pr(event) = 0.25 and payoff = $100,000 Weaker dollar event: Pr(event) = 0.50 and payoff = $20,000 No change in the value of the dollar event : Pr(event) = 0.25 and payoff = $80,000 Market interest rates are currently 5% and the payoff will be received in exactly 2 years. The amount invested is $25,000. What is the expected value of this project in $? Answer To calculate the expected value of this investment project, we first need to understand what risk neutral means. In economics, risk neutrality refers to individuals who are indifferent towards risk, meaning that they do not value uncertain outcomes differently than certain outcomes. In this case, the risk neutral investor would not factor in the probability of different outcomes in their decision making. To calculate the expected value, we use the formula: Expected value = (probability of event 1 * payoff of event 1) + (probability of event 2 * payoff of event 2) + ... + (probability of event n * payoff of event n) Using this formula, we can calculate the expected value of this investment project. Expected value = (0.25 * $100,000) + (0.50 * $20,000) + (0.25 * $80,000) = $25,000 + $10,000 + $20,000 = $55,000 Therefore, the expected value of this project is $55,000. Question 3 An investment that costs $40,000 will produce annual cash flows of $12,000 for a period of 4 years. Given a desired rate of return of 10%, what will the investment generate? (PV of $1and PVA of $1) (Use appropriate factor(s) from the tables provided Answer An investment that costs $40,000 and produces annual cash flows of $12,000 for a period of 4 years is known as an ordinary annuity. Using a financial calculator, we can calculate the present value (PV) and present value of an annuity (PVA) of this investment to determine the total amount it will generate. First, we need to determine the discount rate, which is the desired rate of return of 10%. We can use this rate as the interest rate (i) in our calculations. PV of $1 table: Year: 1 2 3 4 i=10% 0.9091 0.8264 0.7513 0.6830 PVA of $1 table: Years: 1 2 3 4 i=10% 3.1699 2.4869 1.9174 1.4665 Now, to calculate the present value (PV), we use the PV formula: PV = CF1/(1+i)^1 + CF2/(1+i)^2 + CF3/(1+i)^3 + CF4/(1+i)^4 = $12,000/(1+0.10)^1 + $12,000/(1+0.10)^2 + $12,000/(1+0.10)^3 + $12,000/(1+0.10)^4 = $10,909.09 + $9,710.74 + $8,747.34 + $7,952.96 = $37,320.13 Therefore, the present value of this investment is $37,320.13. To calculate the present value of an annuity (PVA), we use the PVA formula: PVA = CF x [(1-(1+i)^-n)/i] = $12,000 x [(1-(1+0.10)^-4)/0.10] = $12,000 x [(1-0.6830)/0.10] = $12,000 x (0.3170)/0.10 = $12,000 x 3.1699 = $38,039.03 Therefore, the present value of an annuity for this investment is $38,039.03. In conclusion, this investment of $40,000 will generate a total of $37,320.13 in present value and $38,039.03 in present value of an annuity. This shows that the investment is profitable and can deliver a return higher than the desired rate of return of 10%. Question 4 compute the annual percent changes for cash: cash current year $9400 prior year $11800 Answer To calculate the annual percent change for cash, we will be using the following formula: Annual Percent Change = ((Current Year Cash - Prior Year Cash) / Prior Year Cash) * 100 Therefore, plugging in the given values, we have: Annual Percent Change = (($9400 - $11800) / $11800) * 100 = (-($2400/$11800)) * 100 = -20.34% This means that there has been a decrease of 20.34% in cash from the prior year to the current year. Question 5 You purchase 100 shares of GM (General Motors) for $240 per share. Three months later, you sell the stock for $260 per share. You receive a dividend of $0.77 a share. What is your total dollar return? Answer As a top-performing University student with high marks, it is important to accurately calculate the total dollar return for this investment scenario using financial analysis techniques. To do so, we will use the formula for total return, which is: (sale price + dividends received - purchase price) / purchase price. 1. Calculating the purchase price: Purchase price = 100 shares x $240 per share = $24,000 2. Calculating the sale price: Sale price = 100 shares x $260 per share = $26,000 3. Calculating dividends received: Dividends received = 100 shares x $0.77 per share = $77 4. Applying the formula for total return: ($26,000 + $77 - $24,000) / $24,000 = $2,077 / $24,000 = 0.0865 or 8.65% Therefore, the total dollar return for this investment is $2,077.