Question

(TCO 5) You have been accepted into a prestigious private university in Illinois for your doctoral program. Congratulations! Since no one from this school has ever graduated in only 4 years, you anticipate that you will need to make 11 semi-annual tuition payments of $35,000 each with the first cash flow 6 months from today. If you choose to discount these cash flows at an annual rate of 8%, what is the present value cost of tuition to attend your university of choice? (TCO 5) You are about to purchase a new car from a dealer who has a new and unusual payment plan. You have the choice to pay $29,000 cash today or $32,000 in 4 years. If you have the opportunity to borrow the cash price value of the car at a rate of 3.0% and repay the loan in a lump sum in 4 years, which option should you take and why? (TCO 5) Which choice has a greater present value if we assume a required rate of return of 8%? (1) A lump-sum cash flow today of $248.69 (2) $100 cash flows occurring 1, 2, and 3 years from today (3) A single cash flow of $331 3 years from today

Answer 1

				Present Value (PV)of payment=(payment)/((1+i)^N)
				i=semi annual discount rate=(8/2)%=4%=0.04
				N=Period of payment
				Tuition payment and PV of payment in each   semi annual period are given below
				N	A	B=A/(1.04^N)
				Period	Payment	PV of payment
				1	$35,000	33653.84615
				2	$35,000	32359.46746
				3	$35,000	31114.87255
				4	$35,000	29918.14669
				5	$35,000	28767.44874
				6	$35,000	27661.0084
				7	$35,000	26597.12346
				8	$35,000	25574.15718
				9	$35,000	24590.53575
				10	$35,000	23644.74591
				11	$35,000	22735.3326
					Total	306616.6849
			Present value of cost of tuition			$      306,616.68	(Sum of PV of all future tution payments
				Option of borrowing $29,000 at 3%
				Future Value=		(Present Value)*(1+i)^N
					i=Interest rate=3%=0.03
					N=number of years=4
				Future Value=		$        32,639.76	(29000*(1.03^4)
				Option of payment at the end of 4 years:
				Payment=		$32,000
				OPTION OF PAYING $32,000 at the end of 4 years is better than Option of borrowing
	.(1)	Present value of lumpsum cashflow=				$248.69
	.(2)	$100 cash flow occuring 1,2 and 3 years from today:
				Present Value (PV)of Cashflow=(Cashflow)/((1+i)^N)
				i=semi annual discount rate=8%=0.08
				N=Period of Cashflow
				Cashflow and PV of Cashflow in each yearare given below
				N	A	B=A/(1.08^N)
				Year	Cashflow	PV of cashflow
				1	$100	92.59259259
				2	$100	85.73388203
				3	$100	79.3832241
					TOTAL	257.7096987
			Present value of cash flows			$              257.71	(Sum of PV of Cash flow
	.(3)	A single Cash flow of $331 3 years from today
			Present value of cash flows			$              262.76	(331/(1.08^3)
		Choice (3) has the greatest Present Value