Present Value of a Single Amount Problems and Solutions
Previous Lesson: Future Value of a Single Amount Problems
Next Lesson: Future Value of Annuity Problems
Problem 1: Present value intra-year discounting
What is the present value of $1,000 received in two years if the interest rate is?
(a) 12% per year discounted annually
Solution:
1,000 / (1 + 0.12) 2
Answer: $797.19
(b) 12% per year discounted semi-annually
Solution:
1,000 / (1 + 0.12/2) 2*2
Answer: $792.09
(c) 12% per year discounted daily
Solution:
1,000 / (1 + 0.12/365) 2*365
Answer: $786.66
Problem 2: Present value of a single amount
You have just won a $1 million lottery. This new lottery, however, will pay out the award 60 years from today. What is the present value of your award based on a 16% p.a. interest rate?
Solution:
1,000,000 / (1 + 0.16) 60
Answer: $135.68
Problem 3: Using present value formula
$7,000 for 10 years from now at 7% is worth how much today?
Solution:
7,000 / (1 + 0.07) 10
Answer: $3,558.45
Problem 4: Present value table
What is the present value of $84,253 to be received or paid in 5 years discounted at 11% by table and factor formula?
Solution:
84,253 (PVIF 11%, 5)
84,253 (0.5935)
Answer: $50,004.16
Problem 5:
Mr. Nadeem owes a total of $3,060 which includes 12% interest for the three years he borrowed the money. How much did he originally borrow?
Solution:
3,060 / (1 + 0.12) 3
Answer: $2,178.05
Problem 6: Present value annual discounting
If we want $2,000 three years from now and the compounded interest rate is 8%, how much should we invest today?
Solution:
2,000 / (1 + 0.08) 3
Answer: $1,587.66
Problem 7: Present value of a single amount
What is the present value of an offer of $14,000 two years from now if the opportunity cost of capital (discount rate) is 17% per year discounted annually?
Solution:
14,000 / (1 + 0.17) 2
Answer: $10,227.19
Problem 8: Finding interest rate
If you invested $50,000 at one point in time and received back $80,000 ten years later, what annual interest (or growth) rate (compounded annually) would you have obtained?
Solution:
(80,000/50,000) (1/10) – 1
Answer: 4.81%
Problem 9: Intra-year discounting
How much would you have to deposit today to have $10,000 in five years at 6% interest discounted quarterly?
Solution:
10,000 / (1 + 0.06 / 4) 5 * 4
Answer: $7,424.46
Problem 10: Present value discounted monthly
What is the present value of an offer of $15,000 one year from now if the opportunity cost of capital (discount rate) is 12% per year nominal annual rate compounded monthly?
Solution:
15,000 / (1 + 0.12/12) 1*12
Answer: $13,311.74
References
Financial Management: Theory and Practice, Dr Eugene F Brigham & C Micheal Ehrhardt
Fundamentals of Financial Management: Concise Edition, Brigham Houston
The Economist Guide to Financial Management, John Tennet
Financial Management: Core Concepts, Raymond M Brooks
I was searching, I SaW YoUr Blog, I ReAd YouR Blog, You Surprised Me. This is the Day, I HaVe learned a Good Thing by ReaDinG!
Writing is an art, and only few people can do that. I must say that you have awesome talent but you do need to improve more. Anyway, your blog post is nice.
As I web-site possessor I believe the content material here is rattling great , appreciate it for your hard work. You should keep it up forever! Good Luck.
Best view i have ever seen !
It’s amazing to go to see this website and reading the views of all friends about
this paragraph, while I am also eager of getting
knowledge.
Good post! We will be linking to this great article
on our website. Keep up the good writing.
Impressive! Thanks for the post.
Best regards,
Boswell Henneberg
I think this is one of the most important information for me. And i am glad reading your article. But should remark on few general things, The web site style is great, the articles is really great : D. Good job, cheers
You’ve made some decent points there. I checked on the net for additional information about the issue and found most people will go along with your views on this website.
Greetings! Very useful advice within this article! It is the little changes which will make the greatest changes. Thanks a lot for sharing!
Everything is very open with a precise description of the challenges. It was really informative. Your site is very helpful. Many thanks for sharing!
This is a topic which is near to my heart… Take care! Exactly where are your contact details though?
Hey there! This is my first visit to your blog! We are a team
of volunteers and starting a new project in a community in the same
niche. Your blog provided us useful information to work on. You have done a
outstanding job!
I need to to thank you for this wonderful read!! I absolutely enjoyed every bit of it. I’ve got you book marked to look at new stuff you post.
Hello there, I discovered your blog via Google whilst looking for a similar matter, your site got here up, it appears great. I have bookmarked it in my google bookmarks.
Hello There. I found your blog using msn. This is an extremely well written article. I will be sure to bookmark it and come back to read more of your useful information. Thanks for the post.
What’s up it’s me, I am also visiting this site daily, this website is actually nice and the users are in fact sharing good thoughts.
Excellent way of explaining, and fastidious piece of writing to obtain facts regarding my presentation subject, which i am going to deliver in school.