1. HandSewn, Inc. offers hand-made customized promotional items that provide an
ID: 1143082 • Letter: 1
Question
1. HandSewn, Inc. offers hand-made customized promotional items that provide an extra special touch of luxury for their customers. Recently, they have been experiencing high levels of repetitive motion injuries, causing their insurer to raise their liability insurance rates to $50,000 per year for the next five years. HandSewn has been discussing options for reducing their liability insurance rates and has identified an internal program that could reduce their insurance rates. HandSewn’s insurer is willing to reduce the annual insurance rate by $8,000 per year for the next five years, if HandSewn implements these programs. HandSewn’s interest rates is 7.8% compounded annually. a. What would be the maximum amount of money that HandSewn would be willing to pay for the improvement program to make it worthwhile (i.e. to make the savings in insurance cost reductions worthwhile)? Assume for this scenario that all insurance payments are made at the end of each year for the next five years.
b. Consider instead, that insurance payments are made at the start of each of year, again for the next five years. How much more/less would the company be willing to pay for the program in this scenario?
Explanation / Answer
Annual insurance reduction potential (P) = $8000
Time (n) = 5 years
Interest Rate (i) = 7.8%
Possible insurance reduction in 5 years = $8000*5 = $40,000
The objective is to find the present value of $40,000. This is the amount that can be invested today in the internal program to reduce the insurance liability.
a) Since the insurance payments are made at the end of each year for the next five years, the formula that needs to be used here is the present value of ordinary annuity.
PV of ordinary annuity = (P/i) * [ 1 - (1/(1+i)n)]
= (8000/0.078) * [ 1 - (1/(1+0.078)5)]
= $32110.76
Therefore, if insurance payments are made at the end of each year for the next five years, the amount that the firm can invest in the internal program is $32110.76
b) Since the insurance payments are made at the beginning of each year for the next five years, the formula that needs to be used here is the present value of annuity due.
PV of ordinary annuity = (P/i) * [ 1 - (1/(1+i)n)] (1+i)
= (8000/0.078) * [ 1 - (1/(1+0.078)5)] * (1+0.078)
= $34615.40
Therefore, if insurance payments are made at the beginning of each year for the next five years, the amount that the firm can invest in the internal program is $34615.40
In the second scenario, the company will be willing to pay an extra amount that equals;
= $34615.4 - $32110.76
= $2504.64
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