Question

Grady Enterprises is looking at two project opportunities for a parcel of land the company currently owns. The first project is a​ restaurant, and the second project is a sports facility. The projected cash flow of the restaurant is an initial cost of ​$1 comma 410 comma 000 with cash flows over the next six years of ​$230 comma 000 ​(year one), ​$270 comma 000 ​(year two), $ 290 comma 000 ​(years three through​ five), and ​$1 comma 730 comma 000 ​(year six), at which point Grady plans to sell the restaurant. The sports facility has the following cash​ flows: an initial cost of ​$2 comma 350 comma 000 with cash flows over the next four years of ​$430 comma 000 ​(years one through​ three) and ​$2 comma 760 comma 000 ​(year four), at which point Grady plans to sell the facility. The appropriate discount rate for the restaurant is 9.0​% and the appropriate discount rate for the sports facility is 13.0​%. What are the MIRRs for the Grady Enterprises​ projects? What are the MIRRs when you adjust for the unequal​ lives? Do the MIRR adjusted for unequal lives change the decision based on the​ MIRRs? ​Hint: Take all cash flows to the same ending period as the longest project.

If the appropriate reinvestment rate for the restaurant is 9.0​%, what is the MIRR of the restaurant​ project?

2.If the appropriate reinvestment rate for the sports facility is 11.5​%, what is the MIRR of the sports​ facility?

3. What is the MIRR of the restaurant when you adjust for unequal​ lives?

4. What is the MIRR of the sports facility when you adjust for unequal​ lives?

Answer 1

EXCEL funtion :- =MIRR(Cash Flow values, Discount rate, Reinvestment rate)

1. RESTAURANT

Discount rate	9%
Reinvestment rate	9%
Time Period	Cash Flows
0	-1410000
1	230000
2	270000
3	290000
4	290000
5	290000
6	1730000
MIRR	16.37%

FV (Restaurant) = $230,000 × (1.09)5 + $270,000 × (1.09)4 + $290,000 × (1.09)3 + $290,000 × (1.09)2 + $290,000 × (1.09)1 + $1,730,000 × (1.09)0 = $3,501,217.95

MIRR = ($3,501,217.95 / $1,410,000)1/6 – 1 = 16.37%

2. SPORTS FACILITY

Discount rate	13%
Reinvestment rate	11.5%
Time Period	Cash Flows
0	-2350000
1	430000
2	430000
3	430000
4	2760000
MIRR	16.78%

FV (Sports Facility) = $430,000 × (1.13)3 + $430,000 × (1.13)2 + $430,000 × (1.13)1 + $2,760,000 × (1.13)0 = $4,415,412.71

MIRR = ($4,415,412.71 / $2,350,000)1/4 – 1 = 16.78%

3. Adjust the Restaurant project to shorter project's life (4 years)

FV (Restaurant) = $230,000 × (1.09)3 + $270,000 × (1.09)2 + $290,000 × (1.09)1 + $290,000 × (1.09)0 + $290,000 × (1.09)-1 + $1,730,000 × (1.09)-2 = $2,946,905.10

MIRR = ($2,946,905.10 / $1,410,000)1/4 – 1 = 20.24%

3. Adjust the shorter project (Sports Facility) to the longer projects life (6 years):

FV (Sports Facility) = $430,000 × (1.13)5 + $430,000 × (1.13)4 + $430,000 × (1.13)3 + 2,760,000 × (1.13)2 = $5,638,040.49

MIRR = ($5,638,040.49 / $2,350,000)1/6 – 1 = 15.7%

Adjusting for unequal lives changes the decision as:

(a) Comparing 4-year MIRRs of Restaurant (20.24%) and Sports Facility (16.78%) reveals that the Restaurant project is better.

(b) Comparing 6-year MIRRs of Restaurant (16.37%) and Sports Facility (15.70%) reveals that the Restaurant project is better.

However, without adjusting for unequal lives, MIRR of Sports Facility (16.78%) was looking more attractive than MIRR of restaurant (16.37%).