Question

Problem 2

You are thinking about getting a new grill for your backyard entertaining. You have a choice between a Weber Kettle Grill that uses charcoal and a Weber Gas Grill that operates on a natural gas feed from your house. The Kettle grill costs $290 and will last about 5 years. You estimate that you will use $185 worth of charcoal each year with the Kettle grill. The Gas Grill costs $950. It does not require charcoal, but you will spend $80 per year on gas. The Gas Grill will last 8 years. Neither grill has any salvage value at the end of its useful life. Assume you have no strong preferences for food cooked over charcoal versus over a gas flame and that the discount rate is 8%. For simplicity, also assume that you pay the cost of charcoal (or natural gas) once a year, via a single payment at the end of each year. Which grill do you choose? 2 Note. Since the grill is for your private and non-commercial use, taxes and depreciation are not relevant

Answer 1

To decide which grill to choose we need to find equivalent annual cost (EAC) of each grill. Grill with lower EAC should be chosen

To find EAC of each grill, first we need to find NPV of each grill

Calculating NPV and EAC of Kettle grill

Cost of Kettle grill = 290, Yearly cost of charcoal = 185

NPV of costs of Kettle grill = Cost of Kettle grill + Sum of present values of yearly cost of charcoal discounted at 8%

= 290 + 185/(1+8%) + 185/(1+8%)² + 185/(1+8%)³ + 185/(1+8%)⁴ + 185/(1+8%)⁵

= 290 + 171.296 + 158.608 + 146.859 + 135.981 + 125.908 = 1028.652 = 1028.65

Now To find EAC we will use pmt function in excel

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

Using pmt function in excel, we get EAC of kettle grill = 257.63

Calculating NPV and EAC of Gas Grill

Cost of Gas grill = 950, Yearly cost of gas = 80

NPV of costs of Gas grill = Cost of Gas grill + Sum of present values of yearly cost of Gas discounted at 8%

= 950 + 80/(1+8%) + 80/(1+8%)² + 80/(1+8%)³ + 80/(1+8%)⁴ + 80/(1+8%)⁵ + 80/(1+8%)⁶ + 80/(1+8%)⁷ + 80/(1+8%)⁸

= 950 + 74.074 + 68.587 + 63.506 + 58.802 + 54.446 + 50.413 + 46.679 + 43.221 = 1409.728 = 1409.73

Now To find EAC we will use pmt function in excel

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

Using pmt function in excel,we get EAC of gas grill = 245.31

Since Equivalent annual cost of gas grill is lower than the equivalent annual cost of kettle grill, therefore Gas grill should be chosen.