Finance homework questions

Steps to Solve

1. Explain preference for receiving money sooner

Receiving $1 today is better than receiving it in the future due to the time value of money. Money received today can be invested and earn a return, making it worth more than the same amount received later. Additionally, there's a risk that you may not actually receive the money in the future due to unforeseen circumstances.

2. Calculate the future value of a deposit with interest

To find the future value of the $100 deposit, use the formula:

$Future Value = Principal \times (1 + Interest Rate)$.

$Future Value = 100 \times (1 + 0.05) = 100 \times 1.05 = 105$.

3. Determine the value of the fish trade

First, convert the Czech koruna and Thai baht amounts to U.S. dollars: Czech koruna: $\frac{2,000,000}{18.50} \approx $108,108.11$ Thai baht: $\frac{3,000,000}{26.25} = $114,285.71$

The value to you is the difference between the revenue from the Czech producer and the cost from the Thai supplier. $Value = $108,108.11 - $114,285.71 \approx -$6,177.60$

4. Calculate future values of annuities

a. Future value of a ten-year ordinary annuity: Use the formula: $FV = Pmt \times \frac{(1 + r)^n - 1}{r}$, where $Pmt = 1000$, $r = 0.12$, and $n = 10$.

$FV = 1000 \times \frac{(1 + 0.12)^{10} - 1}{0.12} = 1000 \times \frac{(1.12)^{10} - 1}{0.12} \approx 1000 \times \frac{3.1058 - 1}{0.12} \approx 1000 \times 17.5487 \approx $17,548.70$

b. Future value with an additional year's interest:

Multiply the previous FV by $(1 + r)$: $FV = 17,548.70 \times (1 + 0.12) = 17,548.70 \times 1.12 \approx $19,654.54$

c. Future value of a 10-year annuity due:

Use the formula: $FV = Pmt \times \frac{(1 + r)^n - 1}{r} \times (1 + r)$, where $Pmt = 1000$, $r = 0.12$, and $n = 10$. $FV = 1000 \times \frac{(1 + 0.12)^{10} - 1}{0.12} \times (1 + 0.12) \approx 17,548.70 \times 1.12 \approx $19,654.54$

d. Relationship between (b) and (c):

The answers in (b) and (c) are the same. This is because earning an additional year's worth of interest on an ordinary annuity is equivalent to having an annuity due. An annuity due has payments at the beginning of each period, so each payment earns one additional year of interest compared to an ordinary annuity.

5. Compare Kim and Hiroshi's superannuation funds

Kim invests $1,000 per month for 37 years (from age 30 to 67), which is 444 months. Hiroshi invests $2,000 per month for 27 years (from age 40 to 67), which is 324 months. The monthly interest rate is $\frac{0.12}{12} = 0.01$.

Kim's future value: $FV_{Kim} = 1000 \times \frac{(1 + 0.01)^{444} - 1}{0.01} \approx 1000 \times \frac{117.42 - 1}{0.01} \approx $11,642,000$

Hiroshi's future value: $FV_{Hiroshi} = 2000 \times \frac{(1 + 0.01)^{324} - 1}{0.01} \approx 2000 \times \frac{33.54 - 1}{0.01} \approx $6,508,000$

Kim will have more superannuation funds available at retirement.

6. Calculate accumulated amounts with compound interest

The formula for compound interest is: $A = P(1 + r)^n$, where $P = 1500$, $r = 0.07$, and $n$ is the number of years.

1. Three years: $A = 1500(1 + 0.07)^3 = 1500(1.07)^3 \approx 1500 \times 1.225043 \approx $1,837.56$

2. Six years: $A = 1500(1 + 0.07)^6 = 1500(1.07)^6 \approx 1500 \times 1.50073 \approx $2,251.09$

3. Nine years: $A = 1500(1 + 0.07)^9 = 1500(1.07)^9 \approx 1500 \times 1.838458 \approx $2,757.69$

4. Explain the role of the Valuation Principle

The Valuation Principle states that the value of an asset is determined by its competitive market price. Financial managers can use this principle to make decisions by comparing the costs and benefits of a decision in terms of market values. If the value of the benefits exceeds the value of the costs, the decision is a good one, as it increases the value of the firm.

8. Explain the comparability of dollar amounts over time

No, we cannot directly compare dollar amounts received at different points in time without considering the time value of money. We need to discount future dollar amounts to their present value to make them comparable. This involves using an appropriate discount rate that reflects the opportunity cost of capital and the risk associated with the future cash flows.