Question

Today is 1 August 2018. Jimmy is 30 years old today and he is considering purchasing 5,000 units of XYZ shares today (XYZ’s current share price is $20). Jimmy will use his own savings to cover 20% of the purchase cost (i.e., $20,000) and he is planning to borrow the remaining 80% of the purchase cost (i.e., $80,000) using a 5-year personal loan (it starts from 1 August 2018) from MQU Bank. Jimmy now has two loan package to choose between

• Package 1.

– Jimmy will make 60 monthly repayments at the beginning of each month over the following five years (from 1 August 2018 to 31 July 2023) with the first payment being made today. This loan needs to be fully repaid by the end of 5 years (i.e., when Jimmy is 35 years old.).

– This package has an annual fee of $200. The package fee is paid on 1 August of each year during the following five years period (from 1 August 2018 to 31 July 2023). The first one being paid today. – The interest rate of this package is j12 = 10% p.a.

• Package 2.

– Jimmy will make 60 monthly repayments at the beginning of each month over the following five years with the first payment being made today. This loan needs to be fully repaid by the end of 5 years (i.e., when Jimmy is 35 years old.).

– Jimmy can have a one year interest-only-period at the beginning of the mortgage. Jimmy’s repayments will be interest-only1 for the first year (i.e., first 12 payments will be interest-only payments), followed by payments of principal plus interest for the following 4 years.

– This package has an annual fee of $400. The package fee is paid on 1 August of each year during the following five year period (from 1 August 2018 to 31 July 2023). The first one being paid today.

– The interest rate of this package is j12 = 12% p.a. Jimmy also plans to sell all the XYZ shares in 5 years’ time (on 1 August 2023). He predicts that the XYZ share price will grow at a rate of y% p.a.

Jimmy assumes that

y = the Australian 10-year Government Bond Yield for 2017 + 10%. (For example, if the XYZ share price is 30 on 1 August 2018 and y is assumed be 15%, the XYZ share price will be 30 from 1 August 2018 to 31 July 2019 and will be 30 × (1 + 15%) from 1 August 2019 to 31 July 2020.) The Australian 10-year Government Bond Yield for 2017 is 2.63.

Jimmy assumes that XYZ shares will pay a dividend on 1 January and 1 July of each year. Jimmy predicts that there are two potential outcomes for the dividend amount.

• Outcome 1: the dividend amount is assumed to be $1 on 1 January 2019 and will increase at a rate of 5% per half-year.

• Outcome 2: the dividend amount is assumed to be $3 on 1 January 2019 and will increase at a rate of 2% per half-year.

NB: Interest-only repayment means your repayments only cover the interest on the amount you have borrowed, during the interest-only period. For example, if you borrow $1,000 through a fiveyear mortgage on 1 July 2018 with a one year interest-only period at j12 = 6% during the first year (1 July 2018–30 June 2019), your monthly repayment is $1, 000×6%/12 = $5 per month. On 1 July 2019, you need to use the remaining four years to repay the borrowed $1,000. The present value on 1 July 2019 of all payments in the remaining four years should be equal to $1,000.

SHOW ALL STEPS AND WORKING ON EXCEL:

– Calculate the loan repayment amount (excluding the annual fee) for each month of package 1 and package 2.

– Use Goal Seek to find the net borrowing cost for package 1 and package 2 by including the annual fee (expressed as a rate p.a. compounded monthly).

– Use a bar or column chart to compare the loan repayment amount of package 1 and package 2 over the five-year loan period.

Answer 1

	Loan Repayment amount (excluding annual fee)
	Package ONE
	Purchase cost of shares	$100,000	(5000*20)
	Borrowed amount=0.8*100000=	$80,000
	Number of months of repayment	60
	Interest rate for one year	10%
	Monthly interest rate=(10/12)%=	0.00833333
	Monthly payment at beginning of months	$1,685.72	(Using PMT function of excel with Rate=0.0083333,Nper=60,PV=-80000,Type=1(payment at beginning)
	Package TWO
	Purchase cost of shares	$100,000	(5000*20)
	Borrowed amount=0.8*100000=	$80,000
	Number of months of repayment	60
	Interest rate for one year	12%
	Monthly interest rate=(12/12)%=	0.01
	Monthly payment at beginning of monthsfor one year(12 payments)	$800.00	(80000*0.01)
	Monthly payments after one year(48 payment)	$2,085.85	(Using PMT function of excel with Rate=0.01,Nper=48,PV=-80000,Type=1(payment at beginning)
	CALCULATION OF NET BORROWING COST
	PACKAGE ONE
	Month	Initial Cash flow	Monthly Payment	Annual Payment	Net cashFlow	LoanRepayment Amount of Package One
	0	$80,000.00	($1,685.72)	($200)	$78,114.28	($1,885.72)
	1		($1,685.72)		($1,685.72)	($1,685.72)
	2		($1,685.72)		($1,685.72)	($1,685.72)
	3		($1,685.72)		($1,685.72)	($1,685.72)
	4		($1,685.72)		($1,685.72)	($1,685.72)
	5		($1,685.72)		($1,685.72)	($1,685.72)
	6		($1,685.72)		($1,685.72)	($1,685.72)
	7		($1,685.72)		($1,685.72)	($1,685.72)
	8		($1,685.72)		($1,685.72)	($1,685.72)
	9		($1,685.72)		($1,685.72)	($1,685.72)
	10		($1,685.72)		($1,685.72)	($1,685.72)
	11		($1,685.72)		($1,685.72)	($1,685.72)
	12		($1,685.72)	($200)	($1,885.72)	($1,885.72)
	13		($1,685.72)		($1,685.72)	($1,685.72)
	14		($1,685.72)		($1,685.72)	($1,685.72)
	15		($1,685.72)		($1,685.72)	($1,685.72)
	16		($1,685.72)		($1,685.72)	($1,685.72)
	17		($1,685.72)		($1,685.72)	($1,685.72)
	18		($1,685.72)		($1,685.72)	($1,685.72)
	19		($1,685.72)		($1,685.72)	($1,685.72)
	20		($1,685.72)		($1,685.72)	($1,685.72)
	21		($1,685.72)		($1,685.72)	($1,685.72)
	22		($1,685.72)		($1,685.72)	($1,685.72)
	23		($1,685.72)		($1,685.72)	($1,685.72)
	24		($1,685.72)	($200)	($1,885.72)	($1,885.72)
	25		($1,685.72)		($1,685.72)	($1,685.72)
	26		($1,685.72)		($1,685.72)	($1,685.72)
	27		($1,685.72)		($1,685.72)	($1,685.72)
	28		($1,685.72)		($1,685.72)	($1,685.72)
	29		($1,685.72)		($1,685.72)	($1,685.72)
	30		($1,685.72)		($1,685.72)	($1,685.72)
	31		($1,685.72)		($1,685.72)	($1,685.72)
	32		($1,685.72)		($1,685.72)	($1,685.72)
	33		($1,685.72)		($1,685.72)	($1,685.72)
	34		($1,685.72)		($1,685.72)	($1,685.72)
	35		($1,685.72)		($1,685.72)	($1,685.72)
	36		($1,685.72)	($200)	($1,885.72)	($1,885.72)
	37		($1,685.72)		($1,685.72)	($1,685.72)
	38		($1,685.72)		($1,685.72)	($1,685.72)
	39		($1,685.72)		($1,685.72)	($1,685.72)
	40		($1,685.72)		($1,685.72)	($1,685.72)
	41		($1,685.72)		($1,685.72)	($1,685.72)
	42		($1,685.72)		($1,685.72)	($1,685.72)
	43		($1,685.72)		($1,685.72)	($1,685.72)
	44		($1,685.72)		($1,685.72)	($1,685.72)
	45		($1,685.72)		($1,685.72)	($1,685.72)
	46		($1,685.72)		($1,685.72)	($1,685.72)
	47		($1,685.72)		($1,685.72)	($1,685.72)
	48		($1,685.72)	($200)	($1,885.72)	($1,885.72)
	49		($1,685.72)		($1,685.72)	($1,685.72)
	50		($1,685.72)		($1,685.72)	($1,685.72)
	51		($1,685.72)		($1,685.72)	($1,685.72)
	52		($1,685.72)		($1,685.72)	($1,685.72)
	53		($1,685.72)		($1,685.72)	($1,685.72)
	54		($1,685.72)		($1,685.72)	($1,685.72)
	55		($1,685.72)		($1,685.72)	($1,685.72)
	56		($1,685.72)		($1,685.72)	($1,685.72)
	57		($1,685.72)		($1,685.72)	($1,685.72)
	58		($1,685.72)		($1,685.72)	($1,685.72)
	59		($1,685.72)		($1,685.72)	($1,685.72)
	60			($200)	($200.00)	($200.00)
	MONTHLY COST OF PACKAGE ONE	0.8775%	(Using IRR function of excel over the net cash flow)
	Borrowing cost of package 1 (rate per annum compounded monthly)	10.53%	(0.8775%*12)
	CALCULATION OF NET BORROWING COST
	PACKAGE TWO
	Month	Initial Cash flow	Monthly Payment	Annual Payment	Net cashFlow	LoanRepayment Amount of Package Two
	0	$80,000.00	($800.00)	($400)	$78,800.00	($1,200.00)
	1		($800.00)		($800.00)	($800.00)
	2		($800.00)		($800.00)	($800.00)
	3		($800.00)		($800.00)	($800.00)
	4		($800.00)		($800.00)	($800.00)
	5		($800.00)		($800.00)	($800.00)
	6		($800.00)		($800.00)	($800.00)
	7		($800.00)		($800.00)	($800.00)
	8		($800.00)		($800.00)	($800.00)
	9		($800.00)		($800.00)	($800.00)
	10		($800.00)		($800.00)	($800.00)
	11		($800.00)		($800.00)	($800.00)
	12		($2,085.85)	($400)	($2,485.85)	($2,485.85)
	13		($2,085.85)		($2,085.85)	($2,085.85)
	14		($2,085.85)		($2,085.85)	($2,085.85)							50 ($2,085.85) ($2,085.85) ($2,085.85) 51 ($2,085.85) ($2,085.85) ($2,085.85) 52 ($2,085.85) ($2,085.85) ($2,085.85) 53 ($2,085.85) ($2,085.85) ($2,085.85) 54 ($2,085.85) ($2,085.85) ($2,085.85) 55 ($2,085.85) ($2,085.85) ($2,085.85) 56 ($2,085.85) ($2,085.85) ($2,085.85) 57 ($2,085.85) ($2,085.85) ($2,085.85) 58 ($2,085.85) ($2,085.85) ($2,085.85) 59 ($2,085.85) ($2,085.85) ($2,085.85) 60 ($400) ($400.00) ($400.00) MONTHLY COST OF PACKAGE ONE 1.0789% (Using IRR function of excel over the net cash flow) Borrowing cost of package 1 (rate per annum compounded monthly) 12.95% (1.0789%*12)