Question

You would like to vacation in Hawaii for one week each year.
You can buy a time share for a vacation home in Hawaii for $18,500 today and a maintenance fee of $600 per year starting next year. You expect to sell the time share in 10 years for $15,000 .
Alternatively you can just pay for the week vacation each year (starting next year). Each year will cost you $1,500 .

If your investments earn 5% per year (compounded annually) which alternative is cheaper and by how much in present value terms?
Time Share Pay each year

Group of answer choices

Buy the time share it will save you $2,459

Pay each year it will save you $2,252

Pay each year it will save you $2,342

Pay each year it will save you $2,506

Answer 1

Cost of Buying time share (initial value)=   -$18,500  
Annual cost=   -600  
Salvage value=   $15,000  
interest Rate (i)=   5%  
Time (n)=   10  

Present value of Cash inflows (PVIFA) = Annual amount * (1-(1/(1+r)^n) / r      
-600 * (1-(1/(1+0.05)^10))/0.05      
=-4633.040958
      
pv of salvage value = Salvage value/(1+r)^n      
15000/(1+0.05)^10      
=$9,208.70      

NPV = Present value of cash inflow-initial investment + PV of Salvage value      
=(-4633.040958 ) +( -$18,500)+ $9,208.70
=-$13,924.34      
      
Other option       
Week vacation cost=   -1500  
interest Rate (i)=   5%  
Time (n)=   10  

Present value of Cash inflows (PVIFA) = Annual amount * (1-(1/(1+r)^n) / r      
=-1500 * (1-(1/(1+0.05)^10))/0.05      
=-11582.60239      
      
Buy a time share NPV=   -$13,924.34  
Week vacation cost pay each year   -$11,582.60  
      
      
Pay each year is cheaper by = -11582.60+(-13924.34)      
$2,341.74      
      
So pay each year will save    $2,342  

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