FBE 506 Quantitative Methods in Finance # 1

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Java Python FBE 506 Quantitative Methods in Finance

Assignment # 1

1. Solve the following equations:

a. x² + 2x - 8 = 0.

b. x² – 9 = 0

c. x³ - x² + 4x - 4 = 0.

d. x⁵ + 3x² – 8 = 0.

2. Future Value Problem: Find the compounded value of $100 deposited at a rate of 6% for 5 years, if the interest is compounded annually, quarterly, monthly, daily and continuously.

Note: For a discrete compounding, the formula is S = A(1 + r/n )^nt, where S is the compounded value, A is the initial investment, r is the interest rate, n is the number of time the interest is compounded a year, and t is the number of years. If the interest is compounded continuously, the compounding formula is S = Ae^rt.

3. Present Value Problem: An investment is expected to have a return of $22000 at the end of the first year, $28500 at the end of the second year, $32000, at the end of the third year, $18000 at the end of the fourth year, and $12000 at the end of the fifth year. At the end of the fifth year the business is expected to have a market value of $52000. What is the present value of the future returns if the interest rate is 6%? What is the present value of the investment?

Note: The present value of the expected future returns for the next n years is PV = R₁/(1+ r)¹+ R₂/(1+r)²+ R₃/(1+r)³ + ...... +R_{n/(1+r)ⁿ, where PV is the present value, R_i is the return in the i^th year, r is the rate of return or interest rate, and n is the number of years.}

4. Net Present Value Problem: Net present value, NPV is the difference between the value of the initial investment, Io and the present value of investment, PVI. If NPV > 0, the investment is profitable. If NPV < 0, the investment will have a loss. Suppose an investment is expected to have returns of $22000, $28500, $32000, $18000, and $12000 at the end of each year for the next five years. At the end of the fifth year, the business is expected to have a market value of MV = $52000. Given that the initial investment is $120000, what is the net present value of the investment if the discount rate is 6%?

5. Perpetuity: A Perpetuity is a security that yields a stream of annual payments at an annual rate of r forever. The value of the perpetuities is decided by the sum of the present value of the stream of payments for infinite number of years. That is, PV = sum(R/(1+r)^t) when t =∞. Here, R is the annual payments and r is the discount factor. Suppose a perpetuity yields an annual payments of $1 forever. What is the present value of the perpetuity if discount rate is 5%?

6. Internal Rate of Return: Internal rate of return is the interest rate at which NPV = 0 or PVI = I_o.

a. For the present value problem in question 4 find the internal rate of return.

b. Find the rate of return on a $24,000 investment with an annual return of $4,500 for five years and a scrap value of $2,500 at the end of the fifth year