Question

Please answer in EXCEL

Geoffrey decides not to buy the car mentioned earlier. Instead, he is now considering a food delivery service "You, bars, meats" that his friend Gillian has recently started. Gillian has agreed that for a single payment of $78,000 today to help her launch her business, she will provide all the delivery services that Geoffrey needs for his business for the next 5 years. Geoffrey is considering borrowing the full amount from his business account. Suppose that Geoffrey makes level quarterly repayments over the coming 5 years, the first payment being exactly 3 months from today. Again, the interest rate on Geoffrey's account is 4.2% p.a. effective.

(a)Geoffrey believes that the overall benefit from this agreement amounts to $369.52448601134 per week in arrears (this would include money he would have spent on alternative delivery services, estimated additional profits from using Gillian's services, etc).

By considering only the initial cost of $78,000 and this weekly benefit of $369.52448601134, calculate the interest rate that represents the return on this investment, expressed as a nominal annual rate compounding weekly

Gillian has entered the agreement with Geoffrey described above. She estimates that the costs of the delivery services she has promised to Geoffrey (petrol, insurance, wear and tear, etc) amount to $1557.7922862927 per month in advance for the coming 5 years.

(a) If Gillian can borrow/invest money at a rate of 3.7% p.a. effective, what is the equivalent amount today of her future liabilities? Note that this calculation should not involve the payment she receives from Geoffrey today.

(b) The money she receives from Geoffrey can be considered a loan, with repayments being the value of the services she provides in return. What is the
interest rate, expressed as an effective annual rate, she is being charged on this "loan"?

Answer 1

Given:

Single Payment to Gillian = $ 78,000

Tenure = 5 years

Interest rate = 4.2%

Solution 1a:

Overall Benefits from the agreement = $369.52448601134 per week

Initial cost to be considered = $ 78,000

The interest rate that represents the return on this investment, (compounding weekly) can be calculated using RATE function in Excel as shown below:

In this case, Tenure is considered in weeks, as benefits are taken per week and compunding is done weekly.

One year has 52 weeks, Hence Tenure = 5 * 52.1775 weeks = 260.714 weeks

Loan amount	78,000
Weekly Payment	369.524486
Tenure	260.714
Interest rate	0.17%
Annual Interest rate	8.74%

Formulas used are:

RATE(nper, pmt, pv) formula is used, where

nper is the number of periods = 260.714

pmt is the periodic payment value = $369.52448601134

pv is the present value = $ 78,000

The result obtained is interest rate per week, hence to obtain annual interest rate, we have multiplied the result with 52.1775 (Since, one year has 52.1775 weeks)

Hence, the required Annual Interest rate is 8.74%

Solution a:

Cost of services = $ 1557.7922862927 per month

Interest rate = 3.7%

Tenure = 5 years = 60 months

The equivalent amount today of her future liabilities can be calculated using the Present Value (PV) formula in Excel as follows:

Cost of Services	1557.792286
Interest rate per annum	3.70%
Interest rate per month	0.003083333
Tenure (months)	60
Present Value of future Liabilities	$85,211.64

Formula used as follows:

PV(rate, nper, pmt) formula has been used where

rate is the interest rate per period = 0.037

nper is number of periods = 60

pmt is te periodic payment value= 1557.7922862927

Hence, the Present Value of the Future Liabilities is $ 85,211.64

Solution b:

The money she receives from Geoffrey can be considered a loan, Hence Loan amount = $ 78,000

Repayments are the value of the services she provides in return. Hence, Repayment = $ 1557.7922862927 per month.

Tenure = 5 years = 5*12 = 60 months

Effective annual rate, she is being charged on this "loan"=?

Interest rate can be calculated using RATE function in Excel as follows:

Loan amount	78,000
Repayment	1557.792
Tenure (months)	60
Interest rate per month	0.61%
Interest rate per annum	7.36%

Formula used in Excel:

RATE(nper, pmt, pv) formula is used, where

nper is the number of periods = 60

pmt is the periodic payment value = $ 1557.7922862927

pv is the present value = $ 78,000

The result obtained is interest rate per month, hence to obtain annual interest rate, we have multiplied the result with 12 (Since, one year has 12 months)

Hence, effective annual rate, she is being charged on this "loan" = 7.36%