Question

Provide Sue with financial advice on which option has the potential to yield the highest monetary value. Support your rational with calculations using time value of money and comment on the risk return relationship for each option, assume interest rate on savings is 4% and is compounded semi-annually.

Sue James is a 55-year old accountant who works at Ernst and Young (EY) who is about to retire. She has the following decision to make:

Option A – Select a lump sum gratuity payment of $120,000 with a reduced pension of $1,750 per month.

Option B – Select a monthly pension of $3,300 with no lump sum gratuity payment.

In addition, Sue has a loan of $72,000 with loan payments of $1,200 per month for the next five years.

Answer 1

Solution:

Savings Interest (Semi Annually)	4%
Lumpsum Gratuity	120000
Loan Outstanding	72000
EMI	1200	pm
	Option A	Option B
Monthly Pension	1750	3300
Loan Repayment	0	1200
Amount left from monthly receipts	1750	2100
Accummulated balance every 6 months,P	10500	12600
Amount at the end of 5 years compounded Semiannually, Future value of annuity	=P*((1+r)^n-1)/r
where P=10500 and 12600; r=2% (4%/2)and n=10 (5*2)
	=10500*((1+2%)^10-1)/.02	=12600*((1+2%)^10-1)/.02
	114972	137966
PV of the above discounted at 4%	FV/(1+r)^n
	=114972/1.04^5	=137966/1.04^5
	94499	113398	A
Lumpsum Gratuity net of Loan repayment	=120000-72000	0
	48000	0
Amount at the end of 5 years compounded Semiannually	P*(1+r)^n where r =2% (4%/2) and n=10 (5*2) semi annual compounding
	=48000*(1+0.02)^10	0
	58512	0
PV of the above discounted at 4%	FV/(1+r)^n
	=58512/(1+0.04)^5	0
	48093	0	B
Total of the PV's of cashflows	142591	113398	A+B
Hence Option A is beneficial

Upfront repayment of loan out of lumpsum gratuity amount is advisable.