Question

A vehicle costs $10,000 when new and has a trade-in value of $7,200 at the end of four years. Its operating expense is $4,000 per year with an additional $2,000 for tires, tune up and battery at the end of the second year. All values are given in today's dollars. What is the equivalent annual cost of owning this vehicle for four years assuming a 10% market interest rate and expected inflation of 2%?

Answer 1

Cash flow in year 0 = - Vehicle cost = -$10000

Cash flow in year 1 = - Operating expenses in year 1 = -$4000

Cash flow in year 2 = - Operating expense in year 1 x (1+ Inflation) - Additional cost = -4000 x (1 + 2%) =-4080 - 2000 = -6080

Cash flow in year 3 = -Operating expense in year 1 x (1+Inflation)² = -4000 x (1+2%)² = -4000 x 1.0404 = -4161.60

Cash flow in year 4 = - Operating expenses in year 1 x (1+inflation)³ + Trade in value = - 4000 x (1+2%)³ + 7200 = -4000 x 1.0612080 + 7200 = -4244.832 + 7200 = 2955.168

Discount rate = 10%

Present value of cash flow = Cash flow / (1+discount rate)^{year of cash flow}

Net Present value of cash flows = Cash flow in year 0 + Present value of cash flows for 1 to 4 discounted at 12% = -10000 -4000 / (1+10%)¹ - 6080 / (1+10%)² - 4161.60 / (1+10%)³ + 2955.168 / (1+10%)⁴ = -10000 - 3636.3636 - 5024.7933 - 3439.3388 + 2018.4195 = -20082.0762

We will find the equivalent annual cash flow of vehicle using PMT function in excel

Formula to be used in excel: =PMT(rate,nper,-pv)

Using PMT function in excel, we get equivalent annual cash flow = -6335.3087

Equivalent annual cost = 6335.3087 = 6335.31 (rounded to two decimal places)

Hence Equivalent annual cost of owning the vehicle = 6335.31