Question

After getting her business degree and working for 5 years and with the help of investment partners, Sally Fraser started her own specialty shop in a regional mall, which is one type of alternative real estate investments. Sally's current lease calls for payments of $1,000 at the end of each month for the next 60 months. Now the property owner offers Sally a new 5-year lease which calls for zero rent for 6 months, then rental payments of $1,050 at the end of each month for the next 54 months. Sally's cost of capital is 11 percent. By what absolute dollar amount would accepting the new lease change Sally's theoretical net worth? Show your calculations

Answer 1

The lease payments constitute ordinary annuity (payment at the end of the period)

Present value of ordinary annuity= P*(1-(1+r)^-n)/r

Where P= Periodical payment, r= interest rate (given as 11%/12= 0.916667% per month) and n= number of payments (6)

Current lease:

Given, P=$1,000 and n=60

Present value of current lease =1000*(1-(1+0.00916667)^-60)/0.00916667

=1000*0.42160281/0.009166667 = $45,993.03

Revised lease:

Given, P=$1,050 and n=54

Present value of current lease after 6 months=1050*(1-(1+0.00916667)^-54)/0.00916667

=1050*0.389052971/0.009166667 = $44,564.25

Value now= $44,564.25 /(1+11%/2)= $43,387.07

Change in theoretical net worth= 45,993.03-43,387.07 = $2,605.96 (Increase)