A major automotive company is considering an agreement with a small manufacturer

Question

A major automotive company is considering an agreement with a small manufacturer whereby it would be required to make end-of-the-yearroyalty payments of $500 000 beginning in year 4 and ending in year 8(five years in total). An immediate lump sum payment of $1 500 000 is being considered as an alternative to this royalty scheme.(i)What cost-of-capital rate makes the royalty and lump sum payment alternatives equallyacceptable?(ii)What alternative is preferred if the company’s cost of capital is in fact lower than this break-even rate?

Explanation / Answer

Option 1:

Cost of capital = x%

Present value of total payment in this scheme
= sum of present values of each annual payment discounted at the rate of cost of capital
= 500000/(1+x%)^4 + 500000/(1+x%)^5 + 500000/(1+x%)^6 + 500000/(1+x%)^7 + 500000/(1+x%)^8
= 500000/(1+x%)^3 * [1/(1+x%) + 1/(1+x%)^2 + 1/(1+x%)^3 + 1/(1+x%)^4 + 1/(1+x%)^5]
= 500000/(1+x%)^3 * [(1-(1+x%)^-5))/x%]

Option 2:

Present value of immediate lumpsum is = $1,500,000

For both options to be equally acceptable

500000/(1+x)^3 * [(1-(1+x)^-5))/x] = 1500000

3x * (1+x)^3 = 1-(1+x)^-5

3x * (1+x)^8 = (1+x)^5 - 1

Solving for x in excel you get x = 9%

Alternatively:

Use the IRR formula with values as

Initial: 1500000
year1: 0
year2: 0
year3: 0
year4: -500000
year5: -500000
year6: -500000
year7: -500000
year8: -500000

You get IRR = 9%

If cost of capital is lower than 9% (break-even rate), option 2 is preferred as you can get capital cheaper than 9% to pay off the liability as a lumpsum, rather that at a higher cost in later years.

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