Xanadu Mining is considering three mutually exclusive alternatives as shown in the table below. $MARR$ is 10 percent/year. Based on an internal rate of return analysis, which alternative should be recommended?

$$\begin{array}{|c|c|c|c|c|c|} \hline \text { EOY } & 0 & 1 & 2 & 3 & 4 \\ \hline \text { A001 } & -\$ 210 & \$ 80 & \$ 90 & \$ 100 & \$ 110 \\ \hline \text { B002 } & -\$ 110 & \$ 60 & \$ 60 & \$ 60 & \$ 70 \\ \hline \text { C003 } & -\$ 160 & \$ 80 & \$ 80 & \$ 80 & \$ 80 \\ \hline \end{array}$$

Here are case prices (in dollars) of wines produced by wineries along three of the Finger Lakes.

a) What null and alternative hypotheses would you test for these data? Talk about prices and location, not symbols.

b) Do the conditions for an ANOVA seem to be met here? Why or why not?

A firm is considering three mutually exclusive alternatives as part of a production improvement program. The alternatives are

$$\begin{matrix} \text{ } & \text{A} & \text{B} & \text{C}\\ \text{Installed cost} & \text{\$10,000} & \text{\$15,000} & \text{\$20,000}\\ \text{Annual benefit} & \text{ 1,625} & \text{ 1,530} & \text{ 1,890}\\\text{Useful life (yrs)} & \text{ 10} & \text{ 20} & \text{ 20}\\ \end{matrix}$$

The salvage value of each alternative is zero, At the end of 10 years, Alternative A could be replaced with another A with identical cost and benefits. (a) Which alternative should be selected if interest is 6%. (b) 3% (c) If there is a difference between parts (a) and (b) can you explain it?

On your child’s first birthday, you open an account to fund her college education. You deposit $2,000 to open the account. Each year, on her birthday, you make another deposit, with each being 10 percent larger than the previous deposit. The account pays interest at 5 percent per year compounded annually. How much money is in the account immediately after the deposit on her eighteenth birthday?

On your child’s first birthday, you open an account to fund his college education. You deposit $300 to open the account. Each year, on his birthday, you make another deposit. Each subsequent deposit is 8 percent larger than the previous. The account pays interest at 5 percent/year compounded annually. How much money is in the account immediately after the deposit on his eighteenth birthday?

Carlisle Company has been cited and must invest in equipment to reduce stack emissions or face EPA fines of $18,500 per year. An emission reduction filter will cost$75,000 and will have an expected life of 5 years. Carlisle’s *MARR *is 10 percent/year.

a. What is the present worth of this investment?

b. What is the decision rule for judging the attractiveness of investments based on present worth?

c. Is the filter economically justified?

d. State at least one noneconomic factor that might influence this decision.

Reconsider the data from Problem 56.

a. Plot a graph of PW versus MARR, where MARR varies from 0 percent to 50 percent by 1 percent increments. PW should be on the y-axis and MARR on the x-axis.

b. Explain the significance of the y-axis intercept.

c. Explain the significance of the x-axis intercept.

Reconsider the data from Problem 62.

a. Plot a graph of FW versus $M A R R$, where $M A R R$ varies from 0 percent to 50 percent by 1 percent increments. FW should be on the $y$-axis and $M A R R$ on the $x$-axis.

b. Explain the significance of the $y$-axis intercept.

c. Explain the significance of the $x$-axis intercept.

Reconsider the data from Problem 4. Management has expressed some concern over the life of the project and the impact of possible early termination. As a result, you have developed additional data based on three possible salvage value scenarios. In each case, the possible salvage values progress from $70,000 at EOY 0 to$2,000 at EOY 6. Case 1 is based on a schedule provided by the vendor as shown below. Case 2 is based on a gradient series decline. Case 3 is based on a geometric series decline.

$$\begin{array}{|l|c|c|c|c|c|c|c|} \hline \text { EOY } & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { NCF } & -\$ 70,000 & \$ 30,000 & \$ 30,000 & \$ 30,000 & \$ 30,000 & \$ 30,000 & \$ 30,000 \\ \hline \text { Vendor SV } & \$ 70,000 & \$ 50,000 & \$ 30,000 & \$ 20,000 & \$ 10,000 & \$ 5,000 & \$ 2,000 \\ \hline \end{array}$$

a. Determine the salvage decline rate for the gradient case.

b. Determine the salvage value decline rate for the geometric case.

c. Determine the annual worth for each case for each planning horizon from 1 to 6 by 1.

d. Plot a graph similar to Figure 7.1 depicting your results from c.

Carlisle Company has been cited and must invest in equipment to reduce stack emissions or face EPA fines of $18,500 per year. An emission reduction filter will cost$75,000 and have an expected life of 5 years. Carlisle’s$MARR$ is 10 percent/year.

a. What is the future worth of this investment?

b. What is the decision rule for judging the attractiveness of investments based on future worth?

c. Is the filter economically justified?

Eddie’s Precision Machine Shop is insured for $700,000. The present yearly insurance premium is$1.00 per $100 of coverage. A sprinkler system with an estimated life of 20 years and no salvage value can be installed for$20,000. Annual maintenance costs for the sprinkler system are $400. If the sprinkler system is installed, the system must be included in the shop’s value for insurance purposes, but the insurance premium will reduce to$0.40 per $100 of coverage. Eddie uses a MARR of 15 percent/year.

a. What is the internal rate of return of this investment?

b. What is the decision rule for judging the attractiveness of investments based on internal rate of return?

c. Is the sprinkler system economically justified?

Eddie’s Precision Machine Shop is insured for $700,000. The present yearly insurance premium is$1.00 per $100 of coverage. A sprinkler system with an estimated life of 20 years and no salvage value can be installed for$20,000. Annual maintenance costs for the sprinkler system are $400. If the sprinkler system is installed, the system must be included in the shop’s value for insurance purposes, but the insurance premium will reduce to$0.40 per $100 of coverage. Eddie uses a$MARR$ of 15 percent/year.

a. What is the future worth of this investment?

b. What is the decision rule for judging the attractiveness of investments based on future worth?

c. Is the sprinkler system economically justified?

The annual worth of an alternative can be calculated from the alternative’s: (a) Present worth by multiplying by (A/P,i,n) (b) Future worth by multiplying by (F/A,i,n) (c) Either (a) or (b) (d) Neither (a) nor (b)

Labco Scientific sells high-purity chemicals to universities, research laboratories, and pharmaceutical companies. The company wants to invest in new equipment that will reduce shipping costs by better matching the size of the completed products with the size of the shipping container. The new equipment is estimated to cost $450,000 to purchase and install. How much must Labco save each year for 3 years in order to justify the investment at an interest rate of 10% per year?