Question

Firms A, B, C, and D enter into a financial arrangement. Money flush firm A will pay expanding firms B and C each $2000000 today. B will pay D $4400000 three years from today. C will pay B $1600000 two years from today and D $700000 two years from today. Finally, D will pay A $6400000 six years from today. Calculate the yield rate or interest rate, to the nearest hundredth of a percent, that each firm experiences over the period of their involvement (6 years for A, 3 years for B, 2 years for C, and 4years for D)

No excel spreadsheets please I want to know what are the equations

Answer 1

For A

Cashoutflow today (to B and C) = $4000000  

Cashinflow after 6 years (from D) = $6400000

So, yield r is given by

4000000 *(1+r)^6 = 6400000

=> r= (6400000/4000000)^(1/6)-1 = 0.081483 or 8.15% p.a.

For B

Cashinflow today(from A) = $2000000  

Cashinflow after 2 years (from C) = $1600000

Cashoutflow after 3 years (to D) = $4400000

So, yield r is given by

2000000 + 1600000/(1+r)^2-4400000/(1+r)^3 =0

Solving r= 0.097512 or 9.75% p.a.

For C

Cashinflow today (from A) = $2000000  

Cashoutflow after 2 years (to B) = $1600000

Cashoutflow after 2 years (to D) = $700000

So, yield r is given by

2000000 - 1600000/(1+r)^2-700000/(1+r)^2 =0

Solving r= 0.07238 or 7.24% p.a.

For D

Cashinflow after two years from today (from C) = $700000  

Cashinflow after three years from today (from B) = $440000  

Cashoutflow after 6 years (to A) = $6400000

So, yield r is given by

700000/(1+r)^2 + 4400000/(1+r)^3-6400000/(1+r)^6 =0

Solving r= 0.0749501 or 7.50% p.a.