Question

Part A: New Equipment

1. Rhonda is debating about buying a new ice cream machine for one of her stores. The current machine is valued at $10,000 this year and will generate $2,500 of profit for the store. The value of the machine at the end of the year will be $8,250. Her other option is to purchase a new piece of equipment for $15,000. The new equipment will generate $4,000 in profit and will be valued at $12,500. Calculate the holding period return for both assets.
2. Rhonda also has the option of purchasing a new espresso maker that will allow her to expand her offerings at one location. She has the savings to purchase the equipment, but would lose the 4.5% annual interest that the savings generates. She expects the espresso machine to generate profits of $3,000 each year over the next 5 years. After five years she could sell the machine for $4,000. What is the present value of the machine to her?

1. Based on the holding period returns calculated in Part A.1 which option should Rhonda choose?
2. If she can purchase the espresso machine in Part A.2 for $20,000, should she?

Please show your work so I can understand the formulas. Thank you!!

Answer 1

Part A.1

Rhonda has 2 options .Lets consider option (a)$10000 machine and option (b) $15000 machine

Now holding period return is basically

Where:

• Income – the distributions or cash flows from the investment (e.g., dividends or profits)
• Vn – the ending value of the investment
• V₀ – the beginning value of the investment

so for option  A holding period return is basically = (2500+8250-10000)/10000 =0.075 or 7.5%

and for option B it is basically = ($4000 +$12500 - $15000) /$15000 = 0.1 or 10%

SO Rhonda should choose option B i.e $15000 ice cream machine

Part A.2

Now she can do the investment but as she is using her savings which will generate a interest income , so to compensate that loss she will have to discount her cash flows with 4.5% . In layman terms , if she is going to generate returns in coming years but we have to find its present value today so all the cash flows had to be brought down to todays rate ( read time value of money for more details on this concept)

Now if she is getting 4.5 % interest discount rate will be 4.5%

now Net present value = net cash inflows -net cash outflows

So Net cash outflows = $20000

Net cash inflows = 3000/(1+0.045) + 3000/(1+0.045)^2 +3000/(1+0.045) ^3 + 3000/(1+0.045) ^4

Net Cash inflows = + + ++

for the last year we used 7000 because machine is sold for 4000 + cash inflow of 3000= 7000

=2870.8+2747.2+2628.9+2515.7+5617.1=16379.7 =16380

Net present value =$16380-$20000=-$3620

So the present value is negative , so she shouldn't invest her money for expresso machine she will be in net loss

I hope you understand the answer , even you still have the problem please feel free to reach again