MathProblems
Class
InstitutionalAnalysis
Table 1: Cost of Buying 

Year 
Down Payment (Opportunity Cost) 
Annual Payment 
Present Value (at d=10%) 
0 
$500,000.00 
  
$665,500.00 
1 
  
$1,621,568.43 
$1,474,153.12 
2 
  
$1,621,568.43 
$1,340,139.20 
3 
  
$1,621,568.43 
$1,218,308.36 
Net Present Value of Costs (Discounting for Time): 
$4,698,100.68 

Table 2: Benefits of Reselling Office Space 

  
Resale Value 
  

Year 
Appreciation Scenario (.75) 
Depreciation Scenario (.25) 
Present Value (at d=10%) 
0 
$5,000,000.00 
$5,000,000.00 
  
1 
$5,100,000.00 
$4,900,000.00 
  
2 
$5,306,040.00 
$4,898,040.00 
  
3 
$5,630,812.00 
$4,994,020.40 
  
EMV (Discounting for Risk): 
$5,471,609.67 

PV of Benefits (Discounting for Time): 
$4,110,901.33 

Table 3: Costs of Leasing Office Space 

Year 
Down Payment (Opportunity Cost) 
Annual Payment 
Present Value (at d=10%) 
0 
250,000.00 
  
332,750.00 
1 
  
250,000.00 
227,272.73 
2 
  
250,000.00 
206,611.57 
3 
  
250,000.00 
187,828.70 
Net Present Value of Costs (Discounting for Time): 
$954,463.00 

CBA Decision: 
Cost of Buying 
Cost of Leasing 

  
$587,199.35 
$954,463.00 
Question4 recommendation
Basedon the above calculations of net present value, I would advise themanagement to buy the office space and later resell it since the netpresent value is positive. Net present value being positive impliesthat in three years time the management will start earning profits. The cost of buying the office space and later reselling at a profitis $587,199.35and that of leasing is $954,463.00. We arrive at the cost of buying by taking the cost of buying officespace plus the benefit of reselling the office space. To calculatethe annual payment we use the PMT formula while to calculate thepresent value in the cost of buying you take the down paymentmultiplied by the PVAIF, 10%, 3. In other words it is. In the benefits of reselling table, every year the officeappreciates by 2 percent with a probability of 75 percent while italso depreciates at 2 percent with a probability of 25 percent. EMVis given by which is $5,471,609.67.
Toget the present value of benefits in that same table we use thediscounting factor for 3 years to get $4,110,901.33. In the third table, we multiply the annual payment by the presentvalue interest factor for each year to get the net present value ofleasing the office space. Since the cost of buying is less than thatof leasing, the management should buy the office space.
Question5 Sensitivity Analysis
Discount rate 
common error 
range 
Cost of buying 
Range of cost 
5% 
0.025 
$587,199.35 

15% 
0.075 
$587,199.35 
Basedon the recommendation in question 4, the cost of buying is more validat 5 percent discounting ate since the difference in the range isless at 5 percent than at 15 percent. I would recommend themanagement to buy and later resell the office space at a marketinterest rate of 5 percent in order to get valid and true data. Inarriving at the common error, we take 50 percent of the discountrate. What you get you add/less from the discount rate to get therange. To get the range of the cost we take the percentage rangemultiplied by the cost of buying. In our scenario one where thediscount rate is 5 percent, we will take. Then we add or less the common error from the discount rate to get. After that, we multiply the range with the cost of buying.
Weperform the same steps for the 15 percent discount rate. When weanalyze the data, we find that at 15 percent the cost of buying has agreater range than at 5 percent. This will imply that the 5 percentdiscount rate is more valid (Triantaphyllou, E. A. Sanchez, 2007).
References
Triantaphyllou,E. A. Sanchez (2007). “A Sensitivity Analysis Approach for SomeDeterministic MultiCriteria DecisionMaking Methods”. DecisionSciences 28(1). Doe: 10.1111/j.15405915.1997.tb01306.x [Accessed25^{th}Nov. 2015].